Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
226 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. #21422166 | C2 | semidirect |
| 5. #21422154 | C2 | semidirect |
| 6. #21422145 | C2 | semidirect |
| 7. C59×#1707 | C2 | semidirect |
| 87. C8×C59 | SD32 | semidirect |
| 106. #1707 | D59 | semidirect |
| 130. C59 | #12487 | semidirect |
| 196. C8 | #14273670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426240 | 2 |
| #21426138 | 2 |
| #21422982 | 2 |
| #21422166 | 2 |
| #21422154 | 2 |
| #21422145 | 2 |
| C59×#1707 | 2 |
| #12487 | 59 |