Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q8×Dic151 | C2 | semidirect |
| 3. #23752545 | C2 | semidirect |
| 5. #23752517 | C2 | semidirect |
| 6. #23752436 | C2 | semidirect |
| 8. #23752319 | C2 | semidirect |
| 9. #23752315 | C2 | semidirect |
| 10. #23752266 | C2 | semidirect |
| 11. #451×C151 | C2 | semidirect |
| 131. C151 | #3117 | semidirect |
| 139. #451 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752748 | 2 |
| C2×Q8×Dic151 | 2 |
| #23752545 | 2 |
| #23752531 | 2 |
| #23752517 | 2 |
| #23752436 | 2 |
| #23752351 | 2 |
| #23752319 | 2 |
| #23752315 | 2 |
| #23752266 | 2 |
| #451×C151 | 2 |
| #3117 | 151 |