Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
648 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21427143 | C2 | semidirect |
| 3. #21424933 | C2 | semidirect |
| 4. #21422665 | C2 | semidirect |
| 5. #21421975 | C2 | semidirect |
| 6. #21421943 | C2 | semidirect |
| 7. C2×C59×#327 | C2 | semidirect |
| 10. #16837715 | C4 | semidirect |
| 13. #16837536 | C4 | semidirect |
| 60. C22⋊(C59⋊C8) | C2×C4 | semidirect |
| 66. C22×D4×C59 | C2×C4 | semidirect |
| 74. C2×C4⋊C4×C59 | C2×C4 | semidirect |
| 134. C22⋊Dic59 | D8 | semidirect |
| 263. C2×#327 | D59 | semidirect |
| 300. C59 | #9277 | semidirect |
| 304. C22×D4 | C4×D59 | semidirect |
| 324. C2×C4⋊C4 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434844 | 2 |
| #21427143 | 2 |
| #21424933 | 2 |
| #21422665 | 2 |
| #21421975 | 2 |
| #21421943 | 2 |
| C2×C59×#327 | 2 |
| #9277 | 59 |