Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D23 |
| commutator, socle, cosocle | C22×C23 | C24 |
| Fitting | C23×C22⋊Q8 | C2 |
| prime radical | C23×D23 | C22 |
| hypercenter | C22⋊Q8 | D23 |
| hypocenter | C23 | C2×C22⋊Q8 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D23 | C2 | semidirect |
| 3. C23×C22⋊Q8 | C2 | semidirect |
| 4. #10625117 | C2 | semidirect |
| 5. #10625095 | C2 | semidirect |
| 6. #10625068 | C2 | semidirect |
| 7. #10625067 | C2 | semidirect |
| 8. C4⋊C4×D23 | C2 | semidirect |
| 9. C4⋊C4×D23 | C2 | semidirect |
| 11. #10625049 | C2 | semidirect |
| 13. C2×Q8×C23 | C22 | semidirect |
| 24. C2×Dic46 | C22 | semidirect |
| 25. C2×Dic46 | C22 | semidirect |
| 26. C4⋊C4×C23 | C22 | semidirect |
| 27. C4⋊C4×C23 | C22 | semidirect |
| 32. C4⋊Dic23 | C22 | semidirect |
| 33. C4⋊Dic23 | C22 | semidirect |
| 34. Dic23⋊C4 | C22 | semidirect |
| 35. Dic23⋊C4 | C22 | semidirect |
| 36. Dic23⋊C4 | C22 | semidirect |
| 40. C22×D23 | Q8 | semidirect |
| 64. C22×C23 | C2×Q8 | semidirect |
| 71. C2×D23 | C2×Q8 | semidirect |
| 87. D23 | C22⋊Q8 | direct (N × H) |
| 95. C22⋊Q8 | D23 | direct (N × H) |
| 99. C23 | C2×C22⋊Q8 | semidirect |
| 104. C2×Q8 | C2×D23 | semidirect |
| 119. C4⋊C4 | C2×D23 | semidirect |
| 120. C4⋊C4 | C2×D23 | semidirect |
| 159. C22 | Q8×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D23 | 2 |
| C22×C4×D23 | 2 |
| C23×C22⋊Q8 | 2 |
| #10625117 | 2 |
| #10625095 | 2 |
| #10625068 | 2 |
| #10625067 | 2 |
| C4⋊C4×D23 | 2 |
| C22⋊C4×D23 | 2 |
| #10625049 | 2 |
| C2×C22⋊Q8 | 23 |