Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
532 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21435091 | C2 | semidirect |
| 2. #21434183 | C2 | semidirect |
| 3. #21434097 | C2 | semidirect |
| 4. #21422730 | C2 | semidirect |
| 5. #21422436 | C2 | semidirect |
| 6. #21421958 | C2 | semidirect |
| 7. C59×#1496 | C2 | semidirect |
| 204. #1496 | D59 | semidirect |
| 239. C59 | #10038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435091 | 2 |
| #21434183 | 2 |
| #21434097 | 2 |
| #21422730 | 2 |
| #21422436 | 2 |
| #21421958 | 2 |
| C59×#1496 | 2 |
| #10038 | 59 |