Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#18012770 | C2 | semidirect |
| 3. #23752586 | C2 | semidirect |
| 4. #23752460 | C2 | semidirect |
| 5. #23752419 | C2 | semidirect |
| 6. #23752412 | C2 | semidirect |
| 7. #23752372 | C2 | semidirect |
| 8. #23752351 | C2 | semidirect |
| 9. C4×#14558994 | C2 | semidirect |
| 10. #23752290 | C2 | semidirect |
| 11. D4×Q8×C151 | C2 | semidirect |
| 52. #14558994 | D4 | semidirect |
| 126. C4×C151 | #137 | semidirect |
| 136. C151 | #3278 | semidirect |
| 140. D4×Q8 | D151 | semidirect |
| 265. C4 | #18012770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012770 | 2 |
| #23752883 | 2 |
| #23752586 | 2 |
| #23752460 | 2 |
| #23752419 | 2 |
| #23752412 | 2 |
| #23752372 | 2 |
| #23752351 | 2 |
| C4×#14558994 | 2 |
| #23752290 | 2 |
| D4×Q8×C151 | 2 |
| #3278 | 151 |