Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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×#18012768 | C2 | semidirect |
| 2. Q8×D604 | C2 | semidirect |
| 4. #23752592 | C2 | semidirect |
| 5. #23752471 | C2 | semidirect |
| 6. #23752422 | C2 | semidirect |
| 7. #23752417 | C2 | semidirect |
| 8. #23752375 | C2 | semidirect |
| 9. #23752369 | C2 | semidirect |
| 10. #23752291 | C2 | semidirect |
| 11. C4×SD16×C151 | C2 | semidirect |
| 73. SD16×C151 | D4 | semidirect |
| 123. C4×C151 | #137 | semidirect |
| 134. C151 | #3276 | semidirect |
| 145. C4×SD16 | D151 | semidirect |
| 196. SD16 | D604 | semidirect |
| 261. C4 | #18012768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012768 | 2 |
| Q8×D604 | 2 |
| #23752866 | 2 |
| #23752592 | 2 |
| #23752471 | 2 |
| #23752422 | 2 |
| #23752417 | 2 |
| #23752375 | 2 |
| #23752369 | 2 |
| #23752291 | 2 |
| C4×SD16×C151 | 2 |
| #3276 | 151 |