Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 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. C2×#18012758 | C2 | semidirect |
| 2. #23752760 | C2 | semidirect |
| 3. C4×#14559003 | C2 | semidirect |
| 4. #23752433 | C2 | semidirect |
| 5. #23752425 | C2 | semidirect |
| 6. #23752423 | C2 | semidirect |
| 7. #23752417 | C2 | semidirect |
| 8. #23752409 | C2 | semidirect |
| 9. C4⋊C8×D151 | C2 | semidirect |
| 10. #23752205 | C2 | semidirect |
| 11. #459×C151 | C2 | semidirect |
| 47. #14559003 | D4 | semidirect |
| 135. C4×C151 | #135 | semidirect |
| 150. C151 | #3035 | semidirect |
| 160. #459 | D151 | semidirect |
| 292. C4 | #18012758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012758 | 2 |
| #23752760 | 2 |
| C4×#14559003 | 2 |
| #23752433 | 2 |
| #23752425 | 2 |
| #23752423 | 2 |
| #23752417 | 2 |
| #23752409 | 2 |
| C4⋊C8×D151 | 2 |
| #23752205 | 2 |
| #459×C151 | 2 |
| #3035 | 151 |