Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
412 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. #21431770 | C2 | semidirect |
| 2. #21423133 | C2 | semidirect |
| 4. #21422122 | C2 | semidirect |
| 5. #21422098 | C2 | semidirect |
| 6. #21422040 | C2 | semidirect |
| 7. C59×#2040 | C2 | semidirect |
| 186. #2040 | D59 | semidirect |
| 218. C59 | #12141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21431770 | 2 |
| #21423133 | 2 |
| #21423031 | 2 |
| #21422122 | 2 |
| #21422098 | 2 |
| #21422040 | 2 |
| C59×#2040 | 2 |
| #12141 | 59 |