Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
388 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #21425890 | C2 | semidirect |
| 5. #21424850 | C2 | semidirect |
| 6. #21422179 | C2 | semidirect |
| 7. C59×#1389 | C2 | semidirect |
| 18. #16837211 | C4 | semidirect |
| 144. #1389 | D59 | semidirect |
| 167. C59 | #12944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837523 | 2 |
| #21425890 | 2 |
| #21425831 | 2 |
| #21425825 | 2 |
| #21424850 | 2 |
| #21422179 | 2 |
| C59×#1389 | 2 |
| #12944 | 59 |