Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. #21423621 | C2 | semidirect |
| 5. #21422077 | C2 | semidirect |
| 6. #21422066 | C2 | semidirect |
| 7. C59×#2225 | C2 | semidirect |
| 139. #2225 | D59 | semidirect |
| 167. C59 | #12389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437173 | 2 |
| #21426335 | 2 |
| #21423621 | 2 |
| #21422140 | 2 |
| #21422077 | 2 |
| #21422066 | 2 |
| C59×#2225 | 2 |
| #12389 | 59 |