Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
212 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21426376 | C2 | semidirect |
| 5. #21422167 | C2 | semidirect |
| 6. #21422153 | C2 | semidirect |
| 7. C59×#1364 | C2 | semidirect |
| 65. C59⋊C16 | SD16 | semidirect |
| 105. #1364 | D59 | semidirect |
| 125. C59 | #12456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426376 | 2 |
| #21425927 | 2 |
| #21423496 | 2 |
| #21423482 | 2 |
| #21422167 | 2 |
| #21422153 | 2 |
| C59×#1364 | 2 |
| #12456 | 59 |