Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 8. Q8×#157 | C4 | semidirect |
| 61. C32×Q8 | C4⋊C4 | semidirect |
| 75. #634 | C4⋊C4 | semidirect |
| 101. #157 | #103 | semidirect |
| 184. C32 | #1803 | semidirect |
| 191. Q8 | #3777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#157 | 2 |
| C2×#63784 | 2 |
| #10593553 | 2 |
| C2×#63744 | 2 |
| #10590093 | 2 |
| #1803 | 9 |