Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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. C2×#18012758 | C2 | semidirect |
| 2. #23752882 | C2 | semidirect |
| 3. #23752866 | C2 | semidirect |
| 4. #23752584 | C2 | semidirect |
| 5. #23752440 | C2 | semidirect |
| 6. #23752423 | C2 | semidirect |
| 7. #23752375 | C2 | semidirect |
| 8. #23752354 | C2 | semidirect |
| 9. C4×#14558992 | C2 | semidirect |
| 10. #23752277 | C2 | semidirect |
| 11. #459×C151 | C2 | semidirect |
| 58. #14558992 | D4 | semidirect |
| 127. C4×C151 | #135 | semidirect |
| 140. C151 | #3284 | semidirect |
| 148. #459 | D151 | semidirect |
| 272. C4 | #18012758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012758 | 2 |
| #23752882 | 2 |
| #23752866 | 2 |
| #23752584 | 2 |
| #23752440 | 2 |
| #23752423 | 2 |
| #23752375 | 2 |
| #23752354 | 2 |
| C4×#14558992 | 2 |
| #23752277 | 2 |
| #459×C151 | 2 |
| #3284 | 151 |