Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #28385428 | C2 | semidirect |
| 2. #28385427 | C2 | semidirect |
| 3. #28385411 | C2 | semidirect |
| 4. #28385405 | C2 | semidirect |
| 5. #28385404 | C2 | semidirect |
| 6. #28385394 | C2 | semidirect |
| 18. #20297726 | C4 | semidirect |
| 19. #20297725 | C4 | semidirect |
| 20. #20297721 | C4 | semidirect |
| 22. SD16×C449 | C4 | semidirect |
| 51. C449 | #444 | semidirect |
| 64. SD16 | #14267798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28385428 | 2 |
| #28385427 | 2 |
| #28385411 | 2 |
| #28385405 | 2 |
| #28385404 | 2 |
| #28385394 | 2 |
| #28385361 | 2 |
| #444 | 449 |