Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
273 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10588370 | C2 | semidirect |
| 3. C8×D36 | C2 | semidirect |
| 4. C9×#322 | C2 | semidirect |
| 5. #10588136 | C2 | semidirect |
| 6. #10588136 | C2 | semidirect |
| 7. #10588134 | C2 | semidirect |
| 76. D36 | M16 | semidirect |
| 94. #322 | D9 | semidirect |
| 203. C9 | #1586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D72 | 2 |
| #10588370 | 2 |
| C8×D36 | 2 |
| C9×#322 | 2 |
| #10588136 | 2 |
| #10588134 | 2 |
| #68081 | 3 |