Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
438 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 2. C9×#408 | C2 | semidirect |
| 3. C2×#63396 | C2 | semidirect |
| 4. C2×#63384 | C2 | semidirect |
| 5. C2×#63381 | C2 | semidirect |
| 6. #10588791 | C2 | semidirect |
| 7. C2×#63375 | C2 | semidirect |
| 15. C2×#3675 | C4 | semidirect |
| 16. C2×#3674 | C4 | semidirect |
| 17. C2×#3673 | C4 | semidirect |
| 18. C2×#3672 | C4 | semidirect |
| 131. #408 | D9 | semidirect |
| 296. C9 | #1975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63513 | 2 |
| C9×#408 | 2 |
| C2×#63396 | 2 |
| C2×#63384 | 2 |
| C2×#63381 | 2 |
| #10588791 | 2 |
| C2×#63375 | 2 |
| #70000 | 3 |