Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 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×#18012760 | C2 | semidirect |
| 2. #23752884 | C2 | semidirect |
| 3. #23752882 | C2 | semidirect |
| 4. #23752588 | C2 | semidirect |
| 5. #23752447 | C2 | semidirect |
| 6. #23752413 | C2 | semidirect |
| 7. #23752358 | C2 | semidirect |
| 8. #23752356 | C2 | semidirect |
| 9. C4×#14558994 | C2 | semidirect |
| 10. #23752277 | C2 | semidirect |
| 11. #460×C151 | C2 | semidirect |
| 58. #14558994 | D4 | semidirect |
| 130. C4×C151 | #135 | semidirect |
| 142. C151 | #3287 | semidirect |
| 150. #460 | D151 | semidirect |
| 276. C4 | #18012760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012760 | 2 |
| #23752884 | 2 |
| #23752882 | 2 |
| #23752588 | 2 |
| #23752447 | 2 |
| #23752413 | 2 |
| #23752358 | 2 |
| #23752356 | 2 |
| C4×#14558994 | 2 |
| #23752277 | 2 |
| #460×C151 | 2 |
| #3287 | 151 |