Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21425870 | C2 | semidirect |
| 5. #21422212 | C2 | semidirect |
| 6. #21422211 | C2 | semidirect |
| 7. C59×#2155 | C2 | semidirect |
| 18. #16837183 | C4 | semidirect |
| 41. #14273667 | C2×C4 | semidirect |
| 54. M32×C59 | C2×C4 | semidirect |
| 146. #2155 | D59 | semidirect |
| 172. C59 | #12932 | semidirect |
| 195. M32 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432684 | 2 |
| #21425870 | 2 |
| C2×#16837183 | 2 |
| #21424135 | 2 |
| #21422212 | 2 |
| #21422211 | 2 |
| C59×#2155 | 2 |
| #12932 | 59 |