Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. #28416182 | C2 | semidirect |
| 5. #28416181 | C2 | semidirect |
| 6. #28416180 | C2 | semidirect |
| 7. #332×C233 | C2 | semidirect |
| 91. C233 | #1549 | semidirect |
| 99. #332 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D233 | 2 |
| #28416487 | 2 |
| #28416457 | 2 |
| #28416182 | 2 |
| #28416181 | 2 |
| #28416180 | 2 |
| #332×C233 | 2 |
| #1549 | 233 |