Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
182 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 56 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. #23750659 | C2 | semidirect |
| 2. #23750653 | C2 | semidirect |
| 3. #23750489 | C2 | semidirect |
| 4. #23750473 | C2 | semidirect |
| 5. #23750473 | C2 | semidirect |
| 6. #11924753⋊C8 | C2 | semidirect |
| 46. #11924753 | D8 | semidirect |
| 52. D596 | M16 | semidirect |
| 83. C149 | #1581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750659 | 2 |
| #23750653 | 2 |
| #23750489 | 2 |
| #23750473 | 2 |
| #11924753⋊C8 | 2 |
| #23749707 | 2 |
| #1581 | 149 |