Finite Group DatabasebetaFinite Group DatabasebetaOrder 29888.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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. #28417951 | C2 | semidirect |
| 2. #28417948 | C2 | semidirect |
| 3. #28417946 | C2 | semidirect |
| 4. #28417942 | C2 | semidirect |
| 5. #28417939 | C2 | semidirect |
| 6. #28417939 | C2 | semidirect |
| 7. #28417938 | C2 | semidirect |
| 8. #28417936 | C2 | semidirect |
| 9. #28417931 | C2 | semidirect |
| 10. #28417931 | C2 | semidirect |
| 12. #28417918 | C2 | semidirect |
| 13. C4×C22⋊D467 | C2 | semidirect |
| 14. #28417911 | C2 | semidirect |
| 15. C22⋊Q8×C467 | C2 | semidirect |
| 103. C467 | #542 | semidirect |
| 115. C22⋊Q8 | D467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28417951 | 2 |
| #28417948 | 2 |
| #28417946 | 2 |
| #28417942 | 2 |
| #28417939 | 2 |
| #28417938 | 2 |
| #28417936 | 2 |
| #28417931 | 2 |
| #28417926 | 2 |
| #28417918 | 2 |
| C4×C22⋊D467 | 2 |
| #28417911 | 2 |
| C22⋊Q8×C467 | 2 |
| #542 | 467 |