Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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×#18012760 | C2 | semidirect |
| 2. #23752884 | C2 | semidirect |
| 3. #23752866 | C2 | semidirect |
| 4. #23752585 | C2 | semidirect |
| 5. #23752442 | C2 | semidirect |
| 6. #23752422 | C2 | semidirect |
| 7. #23752407 | C2 | semidirect |
| 8. #23752377 | C2 | semidirect |
| 9. #23752358 | C2 | semidirect |
| 10. C8×D604 | C2 | semidirect |
| 11. C4×SD16×C151 | C2 | semidirect |
| 73. SD16×C151 | D4 | semidirect |
| 129. C4×C151 | #135 | semidirect |
| 140. C151 | #3284 | semidirect |
| 151. C4×SD16 | D151 | semidirect |
| 204. SD16 | D604 | semidirect |
| 272. 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 |
| #23752866 | 2 |
| #23752585 | 2 |
| #23752442 | 2 |
| #23752422 | 2 |
| #23752407 | 2 |
| #23752377 | 2 |
| #23752358 | 2 |
| C8×D604 | 2 |
| C4×SD16×C151 | 2 |
| #3284 | 151 |