Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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. #28385348 | C2 | semidirect |
| 3. #28385347 | C2 | semidirect |
| 4. #28385275 | C2 | semidirect |
| 5. #28385268 | C2 | semidirect |
| 6. #28385251 | C2 | semidirect |
| 7. #104×C449 | C2 | semidirect |
| 9. #20297726 | C4 | semidirect |
| 10. #20297724 | C4 | semidirect |
| 11. #20297723 | C4 | semidirect |
| 12. #20297721 | C4 | semidirect |
| 51. C449 | #444 | semidirect |
| 58. #104 | D449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28385360 | 2 |
| #28385348 | 2 |
| #28385347 | 2 |
| #28385275 | 2 |
| #28385268 | 2 |
| #28385251 | 2 |
| #104×C449 | 2 |
| #444 | 449 |