Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. #23752947 | C2 | semidirect |
| 2. #23752569 | C2 | semidirect |
| 3. #23752560 | C2 | semidirect |
| 4. #23752509 | C2 | semidirect |
| 5. #23752504 | C2 | semidirect |
| 6. #23752427 | C2 | semidirect |
| 8. Q8×C151⋊C8 | C2 | semidirect |
| 9. C4×#14558992 | C2 | semidirect |
| 10. C4×#14558989 | C2 | semidirect |
| 11. #554×C151 | C2 | semidirect |
| 122. C151 | #3361 | semidirect |
| 125. #554 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752947 | 2 |
| #23752569 | 2 |
| #23752560 | 2 |
| #23752509 | 2 |
| #23752504 | 2 |
| #23752427 | 2 |
| #23752407 | 2 |
| Q8×C151⋊C8 | 2 |
| C4×#14558992 | 2 |
| C4×#14558989 | 2 |
| #554×C151 | 2 |
| #3361 | 151 |