Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 19. C32×C42 | C8 | semidirect |
| 50. C3×C42 | C3⋊C8 | semidirect |
| 94. C42 | C3⋊(C3⋊C8) | semidirect |
| 105. C32 | #1325 | semidirect |
| 134. C3 | #67635 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#384 | 2 |
| #10589394 | 2 |
| #67635 | 3 |