Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23752518 | C2 | semidirect |
| 4. #23752510 | C2 | semidirect |
| 5. #23752508 | C2 | semidirect |
| 6. #23752502 | C2 | semidirect |
| 7. #23752494 | C2 | semidirect |
| 8. #23752249 | C2 | semidirect |
| 9. C4⋊C8×D151 | C2 | semidirect |
| 11. #474×C151 | C2 | semidirect |
| 44. #14559003 | Q8 | semidirect |
| 134. C151 | #3076 | semidirect |
| 143. #474 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752767 | 2 |
| C4×#14559003 | 2 |
| #23752518 | 2 |
| #23752510 | 2 |
| #23752508 | 2 |
| #23752502 | 2 |
| #23752494 | 2 |
| #23752249 | 2 |
| C4⋊C8×D151 | 2 |
| #23752205 | 2 |
| #474×C151 | 2 |
| #3076 | 151 |