Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #29508440 | C2 | semidirect |
| 2. #29508064 | C2 | semidirect |
| 3. #29507917 | C2 | semidirect |
| 5. #29507464 | C2 | semidirect |
| 6. #29507446 | C2 | semidirect |
| 7. Q8⋊C8×C241 | C2 | semidirect |
| 95. C241 | #1628 | semidirect |
| 102. Q8⋊C8 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508440 | 2 |
| #29508064 | 2 |
| #29507917 | 2 |
| #29507913 | 2 |
| #29507464 | 2 |
| #29507446 | 2 |
| Q8⋊C8×C241 | 2 |
| #1628 | 241 |