Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
390 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23752542 | C2 | semidirect |
| 4. #23752519 | C2 | semidirect |
| 5. #23752434 | C2 | semidirect |
| 6. #23752368 | C2 | semidirect |
| 8. C4×#14558994 | C2 | semidirect |
| 9. C4×#14558991 | C2 | semidirect |
| 10. #23752265 | C2 | semidirect |
| 11. C2×C4×Q8×C151 | C2 | semidirect |
| 131. C151 | #3108 | semidirect |
| 134. C2×C4×Q8 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752746 | 2 |
| #23752542 | 2 |
| #23752525 | 2 |
| #23752519 | 2 |
| #23752434 | 2 |
| #23752368 | 2 |
| #23752351 | 2 |
| C4×#14558994 | 2 |
| C4×#14558991 | 2 |
| #23752265 | 2 |
| C2×C4×Q8×C151 | 2 |
| #3108 | 151 |