Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #23749733 | C2 | semidirect |
| 4. #23749732 | C2 | semidirect |
| 5. #23749731 | C2 | semidirect |
| 6. C4×#14558726 | C2 | semidirect |
| 7. #23749717 | C2 | semidirect |
| 11. #441×C149 | C2 | semidirect |
| 15. Q16×D149 | C4 | semidirect |
| 108. C149 | #2950 | semidirect |
| 115. #441 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D149 | 2 |
| #23750101 | 2 |
| #23749733 | 2 |
| #23749732 | 2 |
| #23749731 | 2 |
| C4×#14558726 | 2 |
| #23749717 | 2 |
| #23749660 | 2 |
| #23749632 | 2 |
| #23749582 | 2 |
| #441×C149 | 2 |
| #2950 | 149 |