Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #29506430 | C2 | semidirect |
| 2. #29506429 | C2 | semidirect |
| 3. #29506415 | C2 | semidirect |
| 4. #29506414 | C2 | semidirect |
| 5. #29506411 | C2 | semidirect |
| 6. #29506403 | C2 | semidirect |
| 7. #29506402 | C2 | semidirect |
| 8. C2×#21440152 | C2 | semidirect |
| 9. Q16×D479 | C2 | semidirect |
| 10. #29506390 | C2 | semidirect |
| 11. #137×C479 | C2 | semidirect |
| 87. C479 | #578 | semidirect |
| 94. #137 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506430 | 2 |
| #29506429 | 2 |
| #29506415 | 2 |
| #29506414 | 2 |
| #29506411 | 2 |
| #29506403 | 2 |
| #29506402 | 2 |
| C2×#21440152 | 2 |
| Q16×D479 | 2 |
| #29506390 | 2 |
| #137×C479 | 2 |
| #578 | 479 |