Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 176 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. #23750486 | C2 | semidirect |
| 3. #23750473 | C2 | semidirect |
| 4. #23750466 | C2 | semidirect |
| 41. C8×C149 | M16 | semidirect |
| 55. C149 | #1594 | semidirect |
| 97. C8 | #14558746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750659 | 2 |
| #23750486 | 2 |
| #23750473 | 2 |
| #23750466 | 2 |
| #23749707 | 2 |
| #1594 | 149 |