Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23752585 | C2 | semidirect |
| 3. #23752507 | C2 | semidirect |
| 4. #23752503 | C2 | semidirect |
| 5. #23751955 | C2 | semidirect |
| 6. #23751941 | C2 | semidirect |
| 7. Q8⋊C8×C151 | C2 | semidirect |
| 69. Q8×C151 | SD16 | semidirect |
| 98. C151 | #1631 | semidirect |
| 105. Q8⋊C8 | D151 | semidirect |
| 153. Q8 | #14558993 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752884 | 2 |
| #23752585 | 2 |
| #23752507 | 2 |
| #23752503 | 2 |
| #23751955 | 2 |
| #23751941 | 2 |
| Q8⋊C8×C151 | 2 |
| #1631 | 151 |