Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
468 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 128 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×#431 | C2 | semidirect |
| 3. #10588604 | C2 | semidirect |
| 4. #10588136 | C2 | semidirect |
| 18. C4×C8×C9 | C22 | semidirect |
| 20. C4⋊(C9⋊C8) | C22 | semidirect |
| 83. D36 | M16 | semidirect |
| 90. #431 | D9 | semidirect |
| 146. C4×C8 | C2×D9 | semidirect |
| 216. C9 | #1486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D36 | 2 |
| C9×#431 | 2 |
| #10588604 | 2 |
| #10588136 | 2 |
| #70762 | 3 |