Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 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×C22⋊Q8 | C2 |
| prime radical | C2×C22⋊D23 | C22 |
| hypercenter | C22⋊Q8 | D23 |
| hypocenter | C23 | #554 |
| 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. C23×C22⋊Q8 | C2 | semidirect |
| 2. #10625117 | C2 | semidirect |
| 3. Q8×Dic23 | C2 | semidirect |
| 5. C2×C4⋊Dic23 | C2 | semidirect |
| 6. #10625068 | C2 | semidirect |
| 7. C4⋊C4×D23 | C2 | semidirect |
| 8. #10625060 | C2 | semidirect |
| 9. #10625059 | C2 | semidirect |
| 11. #10625049 | C2 | semidirect |
| 43. C22⋊D23 | Q8 | semidirect |
| 80. C22⋊Q8 | D23 | semidirect |
| 86. C23 | #554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊Q8 | 2 |
| #10625117 | 2 |
| Q8×Dic23 | 2 |
| C4×C22⋊D23 | 2 |
| C2×C4⋊Dic23 | 2 |
| #10625068 | 2 |
| C4⋊C4×D23 | 2 |
| #10625060 | 2 |
| #10625059 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| #10625049 | 2 |
| #554 | 23 |