Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
318 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 11. C8×#157 | C4 | semidirect |
| 41. #622 | C4⋊C4 | semidirect |
| 42. C32×C8 | C4⋊C4 | semidirect |
| 43. C3⋊(C3⋊C8) | C4⋊C4 | semidirect |
| 58. #157 | #106 | semidirect |
| 107. C32 | #1844 | semidirect |
| 121. C8 | #3777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63768 | 2 |
| C2×C8×#157 | 2 |
| #10593553 | 2 |
| C2×#63745 | 2 |
| #1844 | 9 |