Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #21426821 | C2 | semidirect |
| 3. #21422765 | C2 | semidirect |
| 4. #21422656 | C2 | semidirect |
| 5. #21421956 | C2 | semidirect |
| 6. #21421925 | C2 | semidirect |
| 7. C59×#1963 | C2 | semidirect |
| 10. #16837778 | C4 | semidirect |
| 11. #16837750 | C4 | semidirect |
| 48. C4×C59⋊C8 | C2×C4 | semidirect |
| 53. C4⋊Q8×C59 | C2×C4 | semidirect |
| 54. #127×C59 | C2×C4 | semidirect |
| 111. C42×C59 | D8 | semidirect |
| 207. #1963 | D59 | semidirect |
| 238. C59 | #9299 | semidirect |
| 246. C4⋊Q8 | C4×D59 | semidirect |
| 251. #127 | C4×D59 | semidirect |
| 331. C42 | #11745669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435011 | 2 |
| #21426821 | 2 |
| #21422765 | 2 |
| #21422656 | 2 |
| #21421956 | 2 |
| #21421925 | 2 |
| C59×#1963 | 2 |
| #9299 | 59 |