Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
182 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23752584 | C2 | semidirect |
| 2. #23752492 | C2 | semidirect |
| 3. #23752290 | C2 | semidirect |
| 4. #23751964 | C2 | semidirect |
| 5. #23751957 | C2 | semidirect |
| 6. #23751956 | C2 | semidirect |
| 49. C151⋊C8 | D8 | semidirect |
| 85. C151 | #1685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752584 | 2 |
| #23752492 | 2 |
| #23752290 | 2 |
| #23751964 | 2 |
| #23751957 | 2 |
| #23751956 | 2 |
| #459×C151 | 2 |
| #1685 | 151 |