Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #21422885 | C2 | semidirect |
| 4. #21422884 | C2 | semidirect |
| 6. #21421929 | C2 | semidirect |
| 7. C59×#1276 | C2 | semidirect |
| 22. #16837150 | C4 | semidirect |
| 23. #16837150 | C4 | semidirect |
| 24. #16837145 | C4 | semidirect |
| 25. #16837145 | C4 | semidirect |
| 164. #1276 | D59 | semidirect |
| 191. C59 | #8935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433162 | 2 |
| #21424924 | 2 |
| #21422885 | 2 |
| #21422884 | 2 |
| #21422756 | 2 |
| #21421929 | 2 |
| C59×#1276 | 2 |
| #8935 | 59 |