Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D83 |
| commutator, socle, cosocle | C23×C83 | C25 |
| Fitting | C83×#2840 | C2 |
| hypercenter | #2840 | D83 |
| hypocenter | C83 | #36675 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #24915654 | C2 | semidirect |
| 2. #24915547 | C2 | semidirect |
| 3. #24915460 | C2 | semidirect |
| 4. #24910745 | C2 | semidirect |
| 5. #24910680 | C2 | semidirect |
| 6. #24909962 | C2 | semidirect |
| 7. C83×#2840 | C2 | semidirect |
| 8. C22×#13050591 | C22 | semidirect |
| 11. C2×Q8×Dic83 | C22 | semidirect |
| 13. #19127643 | C22 | semidirect |
| 14. #19127628 | C22 | semidirect |
| 16. #19127620 | C22 | semidirect |
| 17. #19127619 | C22 | semidirect |
| 19. #19127612 | C22 | semidirect |
| 24. #19127548 | C22 | semidirect |
| 25. #19127546 | C22 | semidirect |
| 76. C24×C83 | #41 | semidirect |
| 131. #2840 | D83 | semidirect |
| 138. C83 | #36675 | semidirect |
| 189. C24 | #13050591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915654 | 2 |
| #24915547 | 2 |
| #24915460 | 2 |
| #24910745 | 2 |
| #24910680 | 2 |
| #24909962 | 2 |
| C83×#2840 | 2 |
| #36675 | 83 |