Finite Group DatabasebetaFinite Group DatabasebetaOrder 29248.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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. #28410550 | C2 | semidirect |
| 2. #28410542 | C2 | semidirect |
| 3. #28410542 | C2 | semidirect |
| 4. #28410530 | C2 | semidirect |
| 5. #28410530 | C2 | semidirect |
| 6. #28410529 | C2 | semidirect |
| 7. #28410529 | C2 | semidirect |
| 8. #28410528 | C2 | semidirect |
| 9. #28410517 | C2 | semidirect |
| 13. C2×#20300720 | C2 | semidirect |
| 14. C4⋊C4×D457 | C2 | semidirect |
| 15. C22⋊Q8×C457 | C2 | semidirect |
| 54. C22⋊D457 | Q8 | semidirect |
| 101. C457 | #554 | semidirect |
| 111. C22⋊Q8 | D457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28410550 | 2 |
| #28410542 | 2 |
| #28410530 | 2 |
| #28410529 | 2 |
| #28410528 | 2 |
| #28410517 | 2 |
| C4×C22⋊D457 | 2 |
| #28410512 | 2 |
| C2×#20300720 | 2 |
| C4⋊C4×D457 | 2 |
| C22⋊Q8×C457 | 2 |
| #554 | 457 |