Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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×#123 | C2 |
| hypercenter | #123 | D23 |
| hypocenter | C23 | #525 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#67290 | C2 | semidirect |
| 2. C22×C4×D23 | C2 | semidirect |
| 3. C23×#123 | C2 | semidirect |
| 4. #10625108 | C2 | semidirect |
| 5. #10625100 | C2 | semidirect |
| 6. #10625067 | C2 | semidirect |
| 7. #10625064 | C2 | semidirect |
| 8. #10625055 | C2 | semidirect |
| 9. #10625053 | C2 | semidirect |
| 10. (C22⋊D23)⋊C4 | C2 | semidirect |
| 11. #10625048 | C2 | semidirect |
| 17. C2×C22⋊D23 | C22 | semidirect |
| 19. C22×Dic23 | C22 | semidirect |
| 25. C2×C4×D23 | C22 | semidirect |
| 26. C2×Dic46 | C22 | semidirect |
| 27. C4⋊C4×C23 | C22 | semidirect |
| 29. C22⋊C4×C23 | C22 | semidirect |
| 33. (C2×D23)⋊C4 | C22 | semidirect |
| 34. Dic23⋊C4 | C22 | semidirect |
| 35. Dic23⋊C4 | C22 | semidirect |
| 36. C4×Dic23 | C22 | semidirect |
| 52. C2×Dic23 | D4 | semidirect |
| 72. C2×D23 | #41 | semidirect |
| 90. #123 | D23 | semidirect |
| 98. C23 | #525 | semidirect |
| 116. C4⋊C4 | C2×D23 | semidirect |
| 122. C22⋊C4 | C2×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67290 | 2 |
| C22×C4×D23 | 2 |
| C23×#123 | 2 |
| #10625108 | 2 |
| #10625100 | 2 |
| #10625067 | 2 |
| #10625064 | 2 |
| #10625055 | 2 |
| #10625053 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| #10625048 | 2 |
| #525 | 23 |