Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×#18012704 | C2 | semidirect |
| 4. #23752518 | C2 | semidirect |
| 5. #23752437 | C2 | semidirect |
| 6. #23752367 | C2 | semidirect |
| 8. #23752316 | C2 | semidirect |
| 9. #23752311 | C2 | semidirect |
| 10. #23752266 | C2 | semidirect |
| 11. #484×C151 | C2 | semidirect |
| 131. C151 | #3117 | semidirect |
| 135. #484 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752748 | 2 |
| C2×#18012704 | 2 |
| #23752530 | 2 |
| #23752518 | 2 |
| #23752437 | 2 |
| #23752367 | 2 |
| #23752353 | 2 |
| #23752316 | 2 |
| #23752311 | 2 |
| #23752266 | 2 |
| #484×C151 | 2 |
| #3117 | 151 |