Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23752588 | C2 | semidirect |
| 2. #23752407 | C2 | semidirect |
| 3. #23752290 | C2 | semidirect |
| 4. #23751962 | C2 | semidirect |
| 5. #23751956 | C2 | semidirect |
| 6. #23751955 | C2 | semidirect |
| 7. #459×C151 | C2 | semidirect |
| 53. C151⋊C8 | D8 | semidirect |
| 92. C151 | #1687 | semidirect |
| 96. #459 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752588 | 2 |
| #23752407 | 2 |
| #23752290 | 2 |
| #23751962 | 2 |
| #23751956 | 2 |
| #23751955 | 2 |
| #459×C151 | 2 |
| #1687 | 151 |