Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
412 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 2. #21425908 | C2 | semidirect |
| 3. #21422136 | C2 | semidirect |
| 4. #21422132 | C2 | semidirect |
| 5. C59×#2165 | C2 | semidirect |
| 16. #16837223 | C22 | semidirect |
| 20. C59×#364 | C22 | semidirect |
| 146. #2165 | D59 | semidirect |
| 167. #364 | C2×D59 | semidirect |
| 172. C59 | #11992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434548 | 2 |
| #21425908 | 2 |
| #21422136 | 2 |
| #21422132 | 2 |
| C59×#2165 | 2 |
| #11992 | 59 |