Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 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 | C24×D149 |
| commutator, socle, cosocle | C22×C149 | C25 |
| Fitting | C22×#41×C149 | C2 |
| hypercenter | C22×#41 | D149 |
| hypocenter | C149 | #3487 |
| LCS | G ▷ C22×C149 ▷ C149 | |
| UCS | C1 ◁ C22 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#18011959 | C2 | semidirect |
| 2. #23750294 | C2 | semidirect |
| 3. #23750282 | C2 | semidirect |
| 4. #23750192 | C2 | semidirect |
| 5. #23750136 | C2 | semidirect |
| 6. #23750103 | C2 | semidirect |
| 7. C22×#41×C149 | C2 | semidirect |
| 9. C2×#14558737 | C22 | semidirect |
| 11. C2×Q8×D149 | C22 | semidirect |
| 12. #18011907 | C22 | semidirect |
| 13. #18011898 | C22 | semidirect |
| 15. #18011890 | C22 | semidirect |
| 16. #18011885 | C22 | semidirect |
| 17. #18011882 | C22 | semidirect |
| 19. Q8×Dic149 | C22 | semidirect |
| 20. C4×C22⋊D149 | C22 | semidirect |
| 43. C2×Q8×C149 | D4 | semidirect |
| 87. C149 | #3487 | semidirect |
| 90. C22×#41 | D149 | semidirect |
| 121. C2×Q8 | C22⋊D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011959 | 2 |
| #23750294 | 2 |
| #23750282 | 2 |
| #23750192 | 2 |
| #23750136 | 2 |
| #23750103 | 2 |
| C22×#41×C149 | 2 |
| #3487 | 149 |