Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#18011932 | C2 | semidirect |
| 2. #23750176 | C2 | semidirect |
| 3. C4×#14558735 | C2 | semidirect |
| 4. #23749850 | C2 | semidirect |
| 5. #23749842 | C2 | semidirect |
| 6. #23749832 | C2 | semidirect |
| 7. #23749826 | C2 | semidirect |
| 8. #23749820 | C2 | semidirect |
| 9. C4⋊C8×D149 | C2 | semidirect |
| 10. #23749620 | C2 | semidirect |
| 11. #461×C149 | C2 | semidirect |
| 47. #14558735 | D4 | semidirect |
| 136. C4×C149 | #135 | semidirect |
| 150. C149 | #3035 | semidirect |
| 158. #461 | D149 | semidirect |
| 292. C4 | #18011932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011932 | 2 |
| #23750176 | 2 |
| C4×#14558735 | 2 |
| #23749850 | 2 |
| #23749842 | 2 |
| #23749832 | 2 |
| #23749826 | 2 |
| #23749820 | 2 |
| C4⋊C8×D149 | 2 |
| #23749620 | 2 |
| #461×C149 | 2 |
| #3035 | 149 |