Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
504 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21422434 | C2 | semidirect |
| 3. #21422039 | C2 | semidirect |
| 4. #21422027 | C2 | semidirect |
| 5. C59×#1465 | C2 | semidirect |
| 88. C2×D236 | M16 | semidirect |
| 108. C4×Dic59 | M16 | semidirect |
| 199. #1465 | D59 | semidirect |
| 227. C59 | #11533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426818 | 2 |
| #21422434 | 2 |
| #21422039 | 2 |
| #21422027 | 2 |
| C59×#1465 | 2 |
| #11533 | 59 |