Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1130 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 403 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. #21426459 | C2 | semidirect |
| 4. C4×#14273659 | C2 | semidirect |
| 5. #21423927 | C2 | semidirect |
| 7. C59×#1726 | C2 | semidirect |
| 11. C4×#11745660 | C4 | semidirect |
| 30. C4×Dic118 | C2×C4 | semidirect |
| 40. #14273659 | C2×C4 | semidirect |
| 41. #14273652 | C2×C4 | semidirect |
| 49. C4×C8×C59 | C2×C4 | semidirect |
| 79. #11745660 | C42 | semidirect |
| 124. #1726 | D59 | semidirect |
| 146. C59 | #20506 | semidirect |
| 169. C4×C8 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11745660 | 2 |
| #21426459 | 2 |
| #21426458 | 2 |
| C4×#14273659 | 2 |
| #21423927 | 2 |
| #21423922 | 2 |
| C59×#1726 | 2 |
| #20506 | 59 |