Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21435095 | C2 | semidirect |
| 3. #21422810 | C2 | semidirect |
| 4. #21422693 | C2 | semidirect |
| 5. #21422608 | C2 | semidirect |
| 6. #21421990 | C2 | semidirect |
| 7. C59×#3138 | C2 | semidirect |
| 47. C4⋊(C59⋊C8) | D4 | semidirect |
| 60. C4⋊Q8×C59 | D4 | semidirect |
| 61. C4⋊Q8×C59 | D4 | semidirect |
| 75. #97×C59 | D4 | semidirect |
| 196. #3138 | D59 | semidirect |
| 231. C59 | #10096 | semidirect |
| 241. C4⋊Q8 | C22⋊D59 | semidirect |
| 242. C4⋊Q8 | C22⋊D59 | semidirect |
| 274. #97 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435095 | 2 |
| #21430203 | 2 |
| #21422810 | 2 |
| #21422693 | 2 |
| #21422608 | 2 |
| #21421990 | 2 |
| C59×#3138 | 2 |
| #10096 | 59 |