Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
308 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. C22×#3708 | C2 | semidirect |
| 3. C22⋊#3708 | C2 | semidirect |
| 4. C4⋊#3708 | C2 | semidirect |
| 5. C4×#3708 | C2 | semidirect |
| 28. #3708 | D4 | direct (N × H) |
| 36. C32×D4 | C16 | semidirect |
| 64. C22×C32 | C2×C16 | semidirect |
| 68. C32×C4 | C2×C16 | semidirect |
| 118. C32 | D4×C16 | semidirect |
| 120. D4 | #3708 | direct (N × H) |
| 137. C22 | C2×#3708 | semidirect |
| 141. C4 | C2×#3708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3708 | 2 |
| D4×C3⋊(C3⋊C8) | 2 |
| C22⋊#3708 | 2 |
| C4⋊#3708 | 2 |
| C4×#3708 | 2 |
| D4×C16 | 9 |