Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 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. #29508152 | C2 | semidirect |
| 2. C2×#21440583 | C2 | semidirect |
| 3. #29507987 | C2 | semidirect |
| 4. #29507530 | C2 | semidirect |
| 5. #29507524 | C2 | semidirect |
| 6. #29507501 | C2 | semidirect |
| 7. #576×C241 | C2 | semidirect |
| 9. C2×D1928 | C22 | semidirect |
| 13. #21440582 | C22 | semidirect |
| 14. C2×#16838745 | C22 | semidirect |
| 15. #21440578 | C22 | semidirect |
| 93. C241 | #2192 | semidirect |
| 95. #576 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508152 | 2 |
| C2×#21440583 | 2 |
| #29507987 | 2 |
| #29507530 | 2 |
| #29507524 | 2 |
| #29507501 | 2 |
| #576×C241 | 2 |
| #2192 | 241 |