Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
318 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 17. #16837217 | C4 | semidirect |
| 150. C59 | #13139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837224 | 2 |
| C2×#16837219 | 2 |
| C2×#16837217 | 2 |
| #21424965 | 2 |
| #21424004 | 2 |
| #21422179 | 2 |
| C59×#1383 | 2 |
| #13139 | 59 |