Finite Group DatabasebetaFinite Group DatabasebetaOrder 19648.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 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×D307 |
| commutator, socle, cosocle | C22×C307 | C24 |
| Fitting | #123×C307 | C2 |
| hypercenter | #123 | D307 |
| hypocenter | C307 | #560 |
| LCS | G ▷ C22×C307 ▷ C307 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23754256 | C2 | semidirect |
| 2. #23754255 | C2 | semidirect |
| 3. #23754242 | C2 | semidirect |
| 4. #23754235 | C2 | semidirect |
| 5. #23754234 | C2 | semidirect |
| 6. #23754233 | C2 | semidirect |
| 7. #23754230 | C2 | semidirect |
| 8. #23754228 | C2 | semidirect |
| 9. #123×C307 | C2 | semidirect |
| 13. C2×D1228 | C22 | semidirect |
| 16. C2×C22⋊D307 | C22 | semidirect |
| 17. C2×C4×D307 | C22 | semidirect |
| 18. C4⋊Dic307 | C22 | semidirect |
| 19. Dic307⋊C4 | C22 | semidirect |
| 24. (C2×D307)⋊C4 | C22 | semidirect |
| 25. C4×Dic307 | C22 | semidirect |
| 27. C22×C4×C307 | C22 | semidirect |
| 28. C4⋊C4×C307 | C22 | semidirect |
| 30. C22⋊C4×C307 | C22 | semidirect |
| 74. C307 | #560 | semidirect |
| 79. #123 | D307 | semidirect |
| 94. C22×C4 | C2×D307 | semidirect |
| 97. C4⋊C4 | C2×D307 | semidirect |
| 104. C22⋊C4 | C2×D307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23754256 | 2 |
| #23754255 | 2 |
| #23754242 | 2 |
| #23754235 | 2 |
| #23754234 | 2 |
| #23754233 | 2 |
| #23754230 | 2 |
| #23754228 | 2 |
| #123×C307 | 2 |
| #560 | 307 |