Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21426819 | C2 | semidirect |
| 3. #21424929 | C2 | semidirect |
| 4. #21422763 | C2 | semidirect |
| 5. #21421954 | C2 | semidirect |
| 6. #21421924 | C2 | semidirect |
| 7. C59×#1517 | C2 | semidirect |
| 10. #16837778 | C4 | semidirect |
| 11. #16837750 | C4 | semidirect |
| 51. C4×C59⋊C8 | C2×C4 | semidirect |
| 55. C4⋊Q8×C59 | C2×C4 | semidirect |
| 56. #127×C59 | C2×C4 | semidirect |
| 119. C4×Dic59 | D8 | semidirect |
| 209. #1517 | D59 | semidirect |
| 238. C59 | #9299 | semidirect |
| 246. C4⋊Q8 | C4×D59 | semidirect |
| 251. #127 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435011 | 2 |
| #21426819 | 2 |
| #21424929 | 2 |
| #21422763 | 2 |
| #21421954 | 2 |
| #21421924 | 2 |
| C59×#1517 | 2 |
| #9299 | 59 |