Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
254 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 111 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. #10593263 | C2 | direct (N × H) |
| 6. C2×#3771 | C4 | semidirect |
| 19. #3771 | C2×C4 | semidirect |
| 69. C2×C32 | #346 | semidirect |
| 93. C32 | C2×#346 | semidirect |
| 120. C2 | #10593263 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3771 | 2 |
| C2×C4×#622 | 2 |
| #10593263 | 2 |
| C2×#346 | 9 |