Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18012771 | C2 | semidirect |
| 2. C2×#18012768 | C2 | semidirect |
| 4. C4⋊Q8×D151 | C2 | semidirect |
| 5. #23752607 | C2 | semidirect |
| 6. #23752606 | C2 | semidirect |
| 7. #23752604 | C2 | semidirect |
| 8. #23752590 | C2 | semidirect |
| 9. #23752583 | C2 | semidirect |
| 10. #23752164 | C2 | semidirect |
| 11. #497×C151 | C2 | semidirect |
| 63. #14558987 | D4 | semidirect |
| 124. Dic151 | #137 | semidirect |
| 130. C151 | #3152 | semidirect |
| 139. #497 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012771 | 2 |
| C2×#18012768 | 2 |
| #23752761 | 2 |
| C4⋊Q8×D151 | 2 |
| #23752607 | 2 |
| #23752606 | 2 |
| #23752604 | 2 |
| #23752590 | 2 |
| #23752583 | 2 |
| #23752164 | 2 |
| #497×C151 | 2 |
| #3152 | 151 |