Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1389 conjugacy classes of subgroups; only the 428 normal subgroups are shown.
This group has 1389 conjugacy classes of subgroups — too many to draw. Only its 428 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator, socle, prime radical, cosocle | C23×C32 | C24 |
| Fitting | C2×C32×C42 | C22 |
| hypercenter | C2×C42 | D32 |
| hypocenter | C32 | #2868 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 33. C32×C42 | Q8 | semidirect |
| 37. C3×C4×Dic3 | Q8 | semidirect |
| 91. C3×C42 | Dic6 | semidirect |
| 92. C3×C42 | Dic6 | semidirect |
| 99. C4×Dic3 | Dic6 | semidirect |
| 104. C32×C4 | C4⋊Q8 | semidirect |
| 108. C3×Dic3 | C4⋊Q8 | semidirect |
| 156. C42 | #627 | semidirect |
| 170. C3×C4 | #869 | semidirect |
| 171. C3×C4 | #888 | semidirect |
| 176. Dic3 | #869 | semidirect |
| 178. C32 | #2868 | semidirect |
| 205. C4 | #63918 | semidirect |
| 207. C3 | #73311 | semidirect |
| 208. C3 | #74356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63918 | 2 |
| #10592634 | 2 |
| C3×#4935 | 2 |
| C3×C42×Dic3 | 2 |
| #10591349 | 2 |
| #74356 | 3 |
| #73311 | 3 |