Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
578 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 191 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. #10593565 | C2 | direct (N × H) |
| 4. C2×#63748 | C2 | semidirect |
| 15. #63748 | C22 | semidirect |
| 114. C2×C32 | #430 | semidirect |
| 147. C32 | C2×#430 | semidirect |
| 190. C2 | #10593565 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3792 | 2 |
| #10593565 | 2 |
| C2×#63748 | 2 |
| C2×#430 | 9 |