Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
168 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 55 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. #29507999 | C2 | semidirect |
| 3. #29507847 | C2 | semidirect |
| 4. #29507470 | C2 | semidirect |
| 5. #29507463 | C2 | semidirect |
| 62. C8×C241 | SD16 | semidirect |
| 79. C241 | #1686 | semidirect |
| 142. C8 | #16838758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29507999 | 2 |
| #29507914 | 2 |
| #29507847 | 2 |
| #29507470 | 2 |
| #29507463 | 2 |
| #29507461 | 2 |
| #492×C241 | 2 |
| #1686 | 241 |