Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
692 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21435083 | C2 | semidirect |
| 2. #21434188 | C2 | semidirect |
| 3. #21429036 | C2 | semidirect |
| 4. #21425015 | C2 | semidirect |
| 5. #21422540 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 7. C59×#1527 | C2 | semidirect |
| 40. #14273727 | D4 | semidirect |
| 41. #14273724 | D4 | semidirect |
| 61. C4⋊(C59⋊C8) | D4 | semidirect |
| 83. #97×C59 | D4 | semidirect |
| 235. #1527 | D59 | semidirect |
| 271. C59 | #10004 | semidirect |
| 321. #97 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435083 | 2 |
| #21434188 | 2 |
| #21429036 | 2 |
| #21425015 | 2 |
| #21422540 | 2 |
| #21421951 | 2 |
| C59×#1527 | 2 |
| #10004 | 59 |