Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23752874 | C2 | semidirect |
| 3. #23752596 | C2 | semidirect |
| 4. #23752459 | C2 | semidirect |
| 5. #23752434 | C2 | semidirect |
| 6. #23752369 | C2 | semidirect |
| 7. #23752360 | C2 | semidirect |
| 8. #23752291 | C2 | semidirect |
| 9. C4×Q16×C151 | C2 | semidirect |
| 64. Q16×C151 | D4 | semidirect |
| 117. C151 | #3277 | semidirect |
| 126. C4×Q16 | D151 | semidirect |
| 170. Q16 | D604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012771 | 2 |
| #23752874 | 2 |
| #23752596 | 2 |
| #23752459 | 2 |
| #23752434 | 2 |
| #23752369 | 2 |
| #23752360 | 2 |
| #23752291 | 2 |
| C4×Q16×C151 | 2 |
| #3277 | 151 |