Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
372 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21425895 | C2 | semidirect |
| 3. #21422059 | C2 | semidirect |
| 4. #21422056 | C2 | semidirect |
| 5. C59×#1567 | C2 | semidirect |
| 91. Dic236 | M16 | semidirect |
| 93. D472 | M16 | semidirect |
| 148. #1567 | D59 | semidirect |
| 173. C59 | #11660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273749 | 2 |
| #21425895 | 2 |
| #21422059 | 2 |
| #21422056 | 2 |
| C59×#1567 | 2 |
| #11660 | 59 |