Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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×#16837818 | C2 | semidirect |
| 2. #21433740 | C2 | semidirect |
| 3. #21426196 | C2 | semidirect |
| 4. #21426179 | C2 | semidirect |
| 5. #21425880 | C2 | semidirect |
| 6. #21425812 | C2 | semidirect |
| 7. C22×D16×C59 | C2 | semidirect |
| 12. C2×#14273666 | C22 | semidirect |
| 13. C2×C16×D59 | C22 | semidirect |
| 15. #16837635 | C22 | semidirect |
| 18. #16837230 | C22 | semidirect |
| 19. #16837228 | C22 | semidirect |
| 20. #16837203 | C22 | semidirect |
| 52. C2×C16×C59 | D4 | semidirect |
| 125. C22×D16 | D59 | semidirect |
| 155. C59 | #33607 | semidirect |
| 179. C2×C16 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837818 | 2 |
| #21433740 | 2 |
| #21426196 | 2 |
| #21426179 | 2 |
| #21425880 | 2 |
| #21425812 | 2 |
| C22×D16×C59 | 2 |
| #33607 | 59 |