Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
786 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 283 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 |
|---|---|---|
| 3. #21424651 | C2 | semidirect |
| 4. #21423957 | C2 | semidirect |
| 6. C42×C59⋊C8 | C2 | semidirect |
| 7. C59×#1839 | C2 | semidirect |
| 29. #14273721 | C8 | semidirect |
| 65. C42×C59 | C2×C8 | semidirect |
| 69. Dic59⋊C4 | C2×C8 | semidirect |
| 101. C59⋊C8 | #126 | semidirect |
| 119. #1839 | D59 | semidirect |
| 144. C59 | C8×#126 | semidirect |
| 196. C42 | C8×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273721 | 2 |
| #21424700 | 2 |
| #21424651 | 2 |
| #21423957 | 2 |
| #21423866 | 2 |
| C42×C59⋊C8 | 2 |
| C59×#1839 | 2 |
| C8×#126 | 59 |