Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
402 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752767 | C2 | semidirect |
| 3. #23752585 | C2 | semidirect |
| 4. #23752564 | C2 | semidirect |
| 5. #23752560 | C2 | semidirect |
| 6. #23752459 | C2 | semidirect |
| 7. #23752311 | C2 | semidirect |
| 8. C4×#14558987 | C2 | semidirect |
| 9. #500×C151 | C2 | semidirect |
| 90. C8×C151 | #41 | semidirect |
| 112. C151 | #3182 | semidirect |
| 116. #500 | D151 | semidirect |
| 203. C8 | #14559005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752767 | 2 |
| #23752763 | 2 |
| #23752585 | 2 |
| #23752564 | 2 |
| #23752560 | 2 |
| #23752459 | 2 |
| #23752311 | 2 |
| C4×#14558987 | 2 |
| #500×C151 | 2 |
| #3182 | 151 |