Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 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. #23752882 | C2 | semidirect |
| 2. D4×Dic302 | C2 | semidirect |
| 3. #23752558 | C2 | semidirect |
| 4. #23752557 | C2 | semidirect |
| 5. #23752493 | C2 | semidirect |
| 6. #23752490 | C2 | semidirect |
| 7. #23752405 | C2 | semidirect |
| 8. #23752336 | C2 | semidirect |
| 9. D8×Dic151 | C2 | semidirect |
| 10. C4×#14558989 | C2 | semidirect |
| 11. #459×C151 | C2 | semidirect |
| 78. Dic302 | D8 | semidirect |
| 99. D4×C151 | #41 | semidirect |
| 131. C151 | #3358 | semidirect |
| 140. #459 | D151 | semidirect |
| 222. D4 | #14559003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752882 | 2 |
| D4×Dic302 | 2 |
| #23752558 | 2 |
| #23752557 | 2 |
| #23752493 | 2 |
| #23752490 | 2 |
| #23752405 | 2 |
| #23752336 | 2 |
| D8×Dic151 | 2 |
| C4×#14558989 | 2 |
| #459×C151 | 2 |
| #3358 | 151 |