Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #29508483 | C2 | semidirect |
| 3. #29507734 | C2 | semidirect |
| 4. #29507690 | C2 | semidirect |
| 5. #29507478 | C2 | semidirect |
| 6. #29507476 | C2 | semidirect |
| 7. #421×C241 | C2 | semidirect |
| 13. #21440640 | C4 | semidirect |
| 14. #21440638 | C4 | semidirect |
| 15. #21440631 | C4 | semidirect |
| 16. #21440629 | C4 | semidirect |
| 38. #16838754 | D4 | semidirect |
| 61. M16×C241 | D4 | semidirect |
| 125. C241 | #1884 | semidirect |
| 130. #421 | D241 | semidirect |
| 176. M16 | C22⋊D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508483 | 2 |
| #29508263 | 2 |
| #29507734 | 2 |
| #29507690 | 2 |
| #29507478 | 2 |
| #29507476 | 2 |
| #421×C241 | 2 |
| #1884 | 241 |