Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
140 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 1. C2×D3592 | C2 | semidirect |
| 2. C2×#20297721 | C2 | semidirect |
| 3. #28385336 | C2 | semidirect |
| 4. #28385302 | C2 | semidirect |
| 5. #28385269 | C2 | semidirect |
| 6. #28385260 | C2 | semidirect |
| 7. #102×C449 | C2 | semidirect |
| 26. D1796 | D4 | semidirect |
| 53. Dic449 | D8 | semidirect |
| 60. C449 | #459 | semidirect |
| 68. #102 | D449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3592 | 2 |
| C2×#20297721 | 2 |
| #28385336 | 2 |
| #28385302 | 2 |
| #28385269 | 2 |
| #28385260 | 2 |
| #102×C449 | 2 |
| #459 | 449 |