Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
414 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 94 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. #10588521 | C2 | semidirect |
| 3. C4×C8×D9 | C2 | semidirect |
| 4. C9×D4⋊C8 | C2 | semidirect |
| 5. D4⋊(C9⋊C8) | C2 | semidirect |
| 6. #10588162 | C2 | semidirect |
| 7. #10588136 | C2 | semidirect |
| 125. D4⋊C8 | D9 | semidirect |
| 286. C9 | #1492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589650 | 2 |
| #10588521 | 2 |
| C4×C8×D9 | 2 |
| C9×D4⋊C8 | 2 |
| D4⋊(C9⋊C8) | 2 |
| #10588162 | 2 |
| #10588136 | 2 |
| #68176 | 3 |