Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
298 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #10590069 | C2 | direct (N × H) |
| 6. C2×#3708 | C4 | semidirect |
| 19. #3708 | C2×C4 | semidirect |
| 75. C2×C32 | #367 | semidirect |
| 96. C32 | C2×#367 | semidirect |
| 119. C2 | #10590069 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3708 | 2 |
| C2×#63576 | 2 |
| #10590069 | 2 |
| C2×#367 | 9 |