Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23752840 | C2 | semidirect |
| 3. #23752520 | C2 | semidirect |
| 4. #23752513 | C2 | semidirect |
| 5. #23752503 | C2 | semidirect |
| 6. #23752498 | C2 | semidirect |
| 7. #23752254 | C2 | semidirect |
| 8. C2×#18012671 | C2 | semidirect |
| 11. #424×C151 | C2 | semidirect |
| 42. #14559004 | Q8 | semidirect |
| 123. C151 | #3084 | semidirect |
| 133. #424 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752840 | 2 |
| #23752692 | 2 |
| #23752520 | 2 |
| #23752513 | 2 |
| #23752503 | 2 |
| #23752498 | 2 |
| #23752254 | 2 |
| C2×#18012671 | 2 |
| #23752214 | 2 |
| #23752209 | 2 |
| #424×C151 | 2 |
| #3084 | 151 |