Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 174 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. C9×#343 | C2 | semidirect |
| 4. #10588234 | C2 | semidirect |
| 5. #10588207 | C2 | semidirect |
| 15. M16×D9 | C4 | semidirect |
| 39. C9×M16 | C2×C4 | semidirect |
| 45. #3667 | C2×C4 | semidirect |
| 93. #343 | D9 | direct (N × H) |
| 181. D9 | #343 | direct (N × H) |
| 199. M16 | C4×D9 | semidirect |
| 224. C9 | C2×#343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D9 | 2 |
| C2×C4⋊C4×D9 | 2 |
| C9×#343 | 2 |
| #10588234 | 2 |
| #10588207 | 2 |
| D3×#343 | 3 |