Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #29507765 | C2 | semidirect |
| 5. #29507489 | C2 | semidirect |
| 6. #29507477 | C2 | semidirect |
| 7. C4×M16×C241 | C2 | semidirect |
| 16. #21440560 | C4 | semidirect |
| 17. #21440558 | C4 | semidirect |
| 95. C241 | #1932 | semidirect |
| 101. C4×M16 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29507765 | 2 |
| #29507733 | 2 |
| C2×#21440570 | 2 |
| #29507699 | 2 |
| #29507489 | 2 |
| #29507477 | 2 |
| C4×M16×C241 | 2 |
| #1932 | 241 |