Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
946 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 946 conjugacy classes of subgroups — too many to draw. Only its 179 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. #21435474 | C2 | semidirect |
| 2. #21434421 | C2 | semidirect |
| 3. #21423247 | C2 | semidirect |
| 4. #21423185 | C2 | semidirect |
| 5. #21422834 | C2 | semidirect |
| 6. #21422547 | C2 | semidirect |
| 7. C59×#3548 | C2 | semidirect |
| 165. #3548 | D59 | semidirect |
| 199. C59 | #18696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435474 | 2 |
| #21434421 | 2 |
| #21423247 | 2 |
| #21423185 | 2 |
| #21422834 | 2 |
| #21422547 | 2 |
| C59×#3548 | 2 |
| #18696 | 59 |