Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
442 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21433172 | C2 | semidirect |
| 3. #21422730 | C2 | semidirect |
| 4. #21422494 | C2 | semidirect |
| 5. #21421966 | C2 | semidirect |
| 6. #21421959 | C2 | semidirect |
| 7. C59×#1551 | C2 | semidirect |
| 170. #1551 | D59 | semidirect |
| 202. C59 | #9371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435091 | 2 |
| #21433172 | 2 |
| #21422730 | 2 |
| #21422494 | 2 |
| #21421966 | 2 |
| #21421959 | 2 |
| C59×#1551 | 2 |
| #9371 | 59 |