Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
464 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 158 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. #23750660 | C2 | semidirect |
| 2. #23750657 | C2 | semidirect |
| 3. #23750653 | C2 | semidirect |
| 4. #23750647 | C2 | semidirect |
| 5. #23750644 | C2 | semidirect |
| 6. #23750597 | C2 | semidirect |
| 7. D149⋊(C22⋊C8) | C2 | semidirect |
| 9. C2×#14558745 | C22 | semidirect |
| 10. C2×D149⋊C8 | C22 | semidirect |
| 11. C4⋊#11924753 | C22 | semidirect |
| 12. C4⋊#11924753 | C22 | semidirect |
| 16. #18011968 | C22 | semidirect |
| 17. C22⋊#11924753 | C22 | semidirect |
| 18. #18011966 | C22 | semidirect |
| 19. C4×#11924753 | C22 | semidirect |
| 69. D596 | M16 | semidirect |
| 114. C149 | #2974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750660 | 2 |
| #23750657 | 2 |
| #23750653 | 2 |
| #23750647 | 2 |
| #23750644 | 2 |
| #23750597 | 2 |
| D149⋊(C22⋊C8) | 2 |
| C4×D4×D149 | 2 |
| #2974 | 149 |