Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23752769 | C2 | semidirect |
| 2. #23752615 | C2 | semidirect |
| 3. #23752584 | C2 | semidirect |
| 4. #23752564 | C2 | semidirect |
| 5. #23752558 | C2 | semidirect |
| 6. #23752456 | C2 | semidirect |
| 7. #23752312 | C2 | semidirect |
| 8. C4×#14558988 | C2 | semidirect |
| 72. C151⋊C8 | #41 | semidirect |
| 112. C151 | #3182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752769 | 2 |
| #23752615 | 2 |
| #23752584 | 2 |
| #23752564 | 2 |
| #23752558 | 2 |
| #23752456 | 2 |
| #23752312 | 2 |
| C4×#14558988 | 2 |
| #532×C151 | 2 |
| #3182 | 151 |