Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21425890 | C2 | semidirect |
| 5. #21422209 | C2 | semidirect |
| 6. #21422178 | C2 | semidirect |
| 7. C4×#108×C59 | C2 | semidirect |
| 15. #16837217 | C4 | semidirect |
| 16. #16837214 | C4 | semidirect |
| 141. C4×#108 | D59 | semidirect |
| 164. C59 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425890 | 2 |
| #21425843 | 2 |
| #21425823 | 2 |
| #21424984 | 2 |
| #21422209 | 2 |
| #21422178 | 2 |
| C4×#108×C59 | 2 |
| #13137 | 59 |