Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
732 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 119 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. #21424941 | C2 | semidirect |
| 3. #21422833 | C2 | semidirect |
| 4. #21422690 | C2 | semidirect |
| 7. C59×#1997 | C2 | semidirect |
| 186. D236 | #101 | semidirect |
| 199. Dic118 | #101 | semidirect |
| 228. #1997 | D59 | semidirect |
| 266. C59 | #8473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437912 | 2 |
| #21424941 | 2 |
| #21422833 | 2 |
| #21422690 | 2 |
| #21422536 | 2 |
| #21422533 | 2 |
| C59×#1997 | 2 |
| #8473 | 59 |