Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
950 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21435011 | C2 | semidirect |
| 2. #21432490 | C2 | semidirect |
| 3. #21424925 | C2 | semidirect |
| 4. #21422764 | C2 | semidirect |
| 5. #21422763 | C2 | semidirect |
| 6. #21421928 | C2 | semidirect |
| 7. C59×#3205 | C2 | semidirect |
| 48. C4⋊(C59⋊C8) | D4 | semidirect |
| 58. C4⋊Q8×C59 | D4 | semidirect |
| 63. #127×C59 | D4 | semidirect |
| 70. C4⋊C8×C59 | D4 | semidirect |
| 125. C4×Dic59 | D8 | semidirect |
| 204. #3205 | D59 | semidirect |
| 238. C59 | #10280 | semidirect |
| 250. C4⋊Q8 | C22⋊D59 | semidirect |
| 263. #127 | C22⋊D59 | semidirect |
| 276. C4⋊C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435011 | 2 |
| #21432490 | 2 |
| #21424925 | 2 |
| #21422764 | 2 |
| #21422763 | 2 |
| #21421928 | 2 |
| C59×#3205 | 2 |
| #10280 | 59 |