Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #23752550 | C2 | semidirect |
| 3. #23752504 | C2 | semidirect |
| 4. #23752499 | C2 | semidirect |
| 5. #23752419 | C2 | semidirect |
| 6. #23752414 | C2 | semidirect |
| 8. #23752317 | C2 | semidirect |
| 9. #23752310 | C2 | semidirect |
| 10. #23752269 | C2 | semidirect |
| 11. #533×C151 | C2 | semidirect |
| 136. C151 | #3116 | semidirect |
| 138. #533 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14559004 | 2 |
| #23752550 | 2 |
| #23752504 | 2 |
| #23752499 | 2 |
| #23752419 | 2 |
| #23752414 | 2 |
| #23752372 | 2 |
| #23752317 | 2 |
| #23752310 | 2 |
| #23752269 | 2 |
| #533×C151 | 2 |
| #3116 | 151 |