Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
602 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #21434036 | C2 | semidirect |
| 3. #21424173 | C2 | semidirect |
| 4. #21422626 | C2 | semidirect |
| 5. #21422625 | C2 | semidirect |
| 6. #21422005 | C2 | semidirect |
| 7. C59×#3094 | C2 | semidirect |
| 52. C22⋊(C59⋊C8) | D4 | semidirect |
| 71. C2×C4⋊C4×C59 | D4 | semidirect |
| 72. C2×C4⋊C4×C59 | D4 | semidirect |
| 81. C22⋊C8×C59 | D4 | semidirect |
| 221. #3094 | D59 | semidirect |
| 260. C59 | #9983 | semidirect |
| 283. C2×C4⋊C4 | C22⋊D59 | semidirect |
| 284. C2×C4⋊C4 | C22⋊D59 | semidirect |
| 304. C22⋊C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434036 | 2 |
| #21432118 | 2 |
| #21424173 | 2 |
| #21422626 | 2 |
| #21422625 | 2 |
| #21422005 | 2 |
| C59×#3094 | 2 |
| #9983 | 59 |