Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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. #28417107 | C2 | semidirect |
| 2. #28416812 | C2 | semidirect |
| 3. #28416635 | C2 | semidirect |
| 4. #28416631 | C2 | semidirect |
| 5. #28416178 | C2 | semidirect |
| 6. #28416164 | C2 | semidirect |
| 7. Q8⋊C8×C233 | C2 | semidirect |
| 75. Q8×C233 | D8 | semidirect |
| 107. C233 | #1621 | semidirect |
| 114. Q8⋊C8 | D233 | semidirect |
| 164. Q8 | D1864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28417107 | 2 |
| #28416812 | 2 |
| #28416635 | 2 |
| #28416631 | 2 |
| #28416178 | 2 |
| #28416164 | 2 |
| Q8⋊C8×C233 | 2 |
| #1621 | 233 |