Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
132 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 51 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. C4×D1796 | C2 | semidirect |
| 3. #28385271 | C2 | semidirect |
| 4. #28385261 | C2 | semidirect |
| 5. #28385260 | C2 | semidirect |
| 6. #28385251 | C2 | semidirect |
| 7. C4×D4×C449 | C2 | semidirect |
| 10. #20297721 | C4 | semidirect |
| 22. D1796 | C2×C4 | semidirect |
| 26. #16813311 | C2×C4 | semidirect |
| 29. D4×C449 | C2×C4 | semidirect |
| 53. C449 | #442 | semidirect |
| 57. C4×D4 | D449 | semidirect |
| 79. D4 | C4×D449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20297721 | 2 |
| C4×D1796 | 2 |
| #28385271 | 2 |
| #28385261 | 2 |
| #28385260 | 2 |
| #28385251 | 2 |
| C4×D4×C449 | 2 |
| #442 | 449 |