Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 240 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. #28417170 | C2 | semidirect |
| 3. #28416636 | C2 | semidirect |
| 4. #28416635 | C2 | semidirect |
| 5. #28416178 | C2 | semidirect |
| 6. #28416167 | C2 | semidirect |
| 7. Q8⋊C8×C233 | C2 | semidirect |
| 98. C233 | #1620 | semidirect |
| 106. Q8⋊C8 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28417170 | 2 |
| #28416812 | 2 |
| #28416636 | 2 |
| #28416635 | 2 |
| #28416178 | 2 |
| #28416167 | 2 |
| Q8⋊C8×C233 | 2 |
| #1620 | 233 |