Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #29508120 | C2 | semidirect |
| 4. #29507464 | C2 | semidirect |
| 5. Q8⋊#14515349 | C2 | semidirect |
| 7. #462×C241 | C2 | semidirect |
| 55. D964 | Q16 | semidirect |
| 92. C241 | #1649 | semidirect |
| 97. #462 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D964 | 2 |
| #29508120 | 2 |
| #29507994 | 2 |
| #29507464 | 2 |
| Q8⋊#14515349 | 2 |
| #29507444 | 2 |
| #462×C241 | 2 |
| #1649 | 241 |