Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10589346 | C2 | semidirect |
| 5. #10589345 | C2 | semidirect |
| 66. C3⋊(C3⋊C8) | M16 | semidirect |
| 154. C32 | #1569 | semidirect |
| 186. C3 | #70492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#423 | 2 |
| #10592625 | 2 |
| C4×#3748 | 2 |
| #10589346 | 2 |
| #10589345 | 2 |
| #70492 | 3 |