Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #23752320 | C2 | semidirect |
| 4. #23752319 | C2 | semidirect |
| 5. #23752318 | C2 | semidirect |
| 6. C4×#14558994 | C2 | semidirect |
| 7. #23752304 | C2 | semidirect |
| 11. #441×C151 | C2 | semidirect |
| 15. Q16×D151 | C4 | semidirect |
| 108. C151 | #2950 | semidirect |
| 115. #441 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D151 | 2 |
| #23752688 | 2 |
| #23752320 | 2 |
| #23752319 | 2 |
| #23752318 | 2 |
| C4×#14558994 | 2 |
| #23752304 | 2 |
| #23752247 | 2 |
| #23752219 | 2 |
| #23752169 | 2 |
| #441×C151 | 2 |
| #2950 | 151 |