Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#18012737 | C2 | semidirect |
| 3. #23752605 | C2 | semidirect |
| 4. #23752579 | C2 | semidirect |
| 5. #23752420 | C2 | semidirect |
| 6. #23752416 | C2 | semidirect |
| 7. #23752367 | C2 | semidirect |
| 10. #23752266 | C2 | semidirect |
| 11. #451×C151 | C2 | semidirect |
| 137. C151 | #3218 | semidirect |
| 146. #451 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012737 | 2 |
| #23752748 | 2 |
| #23752605 | 2 |
| #23752579 | 2 |
| #23752420 | 2 |
| #23752416 | 2 |
| #23752367 | 2 |
| #23752353 | 2 |
| #23752351 | 2 |
| #23752266 | 2 |
| #451×C151 | 2 |
| #3218 | 151 |