Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
678 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 678 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. #21435406 | C2 | semidirect |
| 2. #21435016 | C2 | semidirect |
| 3. #21434548 | C2 | semidirect |
| 4. #21425022 | C2 | semidirect |
| 5. #21425015 | C2 | semidirect |
| 6. #21422592 | C2 | semidirect |
| 7. C59×#1283 | C2 | semidirect |
| 112. M16×C59 | D8 | semidirect |
| 219. #1283 | D59 | semidirect |
| 251. C59 | #10192 | semidirect |
| 337. M16 | D472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435406 | 2 |
| #21435016 | 2 |
| #21434548 | 2 |
| #21425022 | 2 |
| #21425015 | 2 |
| #21422592 | 2 |
| C59×#1283 | 2 |
| #10192 | 59 |