Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23752622 | C2 | semidirect |
| 3. #23752578 | C2 | semidirect |
| 4. #23752530 | C2 | semidirect |
| 5. #23752525 | C2 | semidirect |
| 6. #23752509 | C2 | semidirect |
| 7. #23752269 | C2 | semidirect |
| 8. C2×#125×C151 | C2 | semidirect |
| 106. C151 | #3234 | semidirect |
| 109. C2×#125 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| #23752622 | 2 |
| #23752578 | 2 |
| #23752530 | 2 |
| #23752525 | 2 |
| #23752509 | 2 |
| #23752269 | 2 |
| C2×#125×C151 | 2 |
| #3234 | 151 |