Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21434218 | C2 | semidirect |
| 3. #21425037 | C2 | semidirect |
| 4. #21422708 | C2 | semidirect |
| 5. #21422707 | C2 | semidirect |
| 6. #21421965 | C2 | semidirect |
| 7. C59×#3112 | C2 | semidirect |
| 198. #3112 | D59 | semidirect |
| 234. C59 | #10028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435403 | 2 |
| #21434218 | 2 |
| #21425037 | 2 |
| #21422708 | 2 |
| #21422707 | 2 |
| #21421965 | 2 |
| C59×#3112 | 2 |
| #10028 | 59 |