Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
298 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21426143 | C2 | semidirect |
| 4. #21422154 | C2 | semidirect |
| 5. #21422061 | C2 | semidirect |
| 7. C59×#2241 | C2 | semidirect |
| 98. D236 | Q32 | semidirect |
| 125. #2241 | D59 | semidirect |
| 152. C59 | #12346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436488 | 2 |
| #21426143 | 2 |
| #21423458 | 2 |
| #21422154 | 2 |
| #21422061 | 2 |
| #21422052 | 2 |
| C59×#2241 | 2 |
| #12346 | 59 |