Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 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×#18012759 | C2 | semidirect |
| 2. #23752867 | C2 | semidirect |
| 3. #23752591 | C2 | semidirect |
| 4. #23752451 | C2 | semidirect |
| 5. #23752417 | C2 | semidirect |
| 6. #23752414 | C2 | semidirect |
| 7. #23752374 | C2 | semidirect |
| 8. #23752372 | C2 | semidirect |
| 9. C4×#14558989 | C2 | semidirect |
| 10. D4×C151⋊C8 | C2 | semidirect |
| 11. #547×C151 | C2 | semidirect |
| 53. #14558989 | D4 | semidirect |
| 127. C4×C151 | #135 | semidirect |
| 138. C151 | #3283 | semidirect |
| 142. #547 | D151 | semidirect |
| 268. C4 | #18012759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012759 | 2 |
| #23752867 | 2 |
| #23752591 | 2 |
| #23752451 | 2 |
| #23752417 | 2 |
| #23752414 | 2 |
| #23752374 | 2 |
| #23752372 | 2 |
| C4×#14558989 | 2 |
| D4×C151⋊C8 | 2 |
| #547×C151 | 2 |
| #3283 | 151 |