Finite Group DatabasebetaFinite Group DatabasebetaOrder 29888.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D467 |
| commutator, socle, cosocle | C22×C467 | C24 |
| Fitting | #126×C467 | C2 |
| prime radical | C2×C22⋊D467 | C22 |
| hypercenter | #126 | D467 |
| hypocenter | C467 | #563 |
| LCS | G ▷ C22×C467 ▷ C467 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28417953 | C2 | semidirect |
| 2. #28417952 | C2 | semidirect |
| 3. #28417948 | C2 | semidirect |
| 4. #28417947 | C2 | semidirect |
| 5. #28417946 | C2 | semidirect |
| 6. #28417944 | C2 | semidirect |
| 7. #28417943 | C2 | semidirect |
| 11. #28417933 | C2 | semidirect |
| 12. #28417931 | C2 | semidirect |
| 13. #28417930 | C2 | semidirect |
| 14. #28417930 | C2 | semidirect |
| 15. #126×C467 | C2 | semidirect |
| 97. C467 | #563 | semidirect |
| 104. #126 | D467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28417953 | 2 |
| #28417952 | 2 |
| #28417948 | 2 |
| #28417947 | 2 |
| #28417946 | 2 |
| #28417944 | 2 |
| #28417943 | 2 |
| #28417939 | 2 |
| #28417937 | 2 |
| #28417935 | 2 |
| #28417933 | 2 |
| #28417931 | 2 |
| #28417930 | 2 |
| #126×C467 | 2 |
| #563 | 467 |