Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23752584 | C2 | semidirect |
| 2. #23752507 | C2 | semidirect |
| 3. #23752502 | C2 | semidirect |
| 4. #23751956 | C2 | semidirect |
| 5. Q8⋊(C151⋊C8) | C2 | semidirect |
| 6. D4⋊(C151⋊C8) | C2 | semidirect |
| 58. Q8×C151 | SD16 | semidirect |
| 98. C151 | #1631 | semidirect |
| 153. Q8 | #14558992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752584 | 2 |
| #23752507 | 2 |
| #23752502 | 2 |
| #23751956 | 2 |
| Q8⋊(C151⋊C8) | 2 |
| D4⋊(C151⋊C8) | 2 |
| #550×C151 | 2 |
| #1631 | 151 |