Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
222 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 121 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. #21422232 | C2 | semidirect |
| 4. #21422231 | C2 | semidirect |
| 5. C59×#1398 | C2 | semidirect |
| 10. #16837235 | C4 | semidirect |
| 11. C32×D59 | C4 | semidirect |
| 29. C59⋊C32 | C2×C4 | semidirect |
| 33. C32×C59 | C2×C4 | semidirect |
| 84. #1398 | D59 | direct (N × H) |
| 88. D59 | #1398 | direct (N × H) |
| 100. C59 | C2×#1398 | semidirect |
| 117. C32 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M64×D59 | 2 |
| #346×D59 | 2 |
| #21422232 | 2 |
| #21422231 | 2 |
| C59×#1398 | 2 |
| C2×#1398 | 59 |