Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
598 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #21435214 | C2 | semidirect |
| 3. #21434555 | C2 | semidirect |
| 4. #21425048 | C2 | semidirect |
| 5. #21422590 | C2 | semidirect |
| 6. #21421947 | C2 | semidirect |
| 7. C59×#1980 | C2 | semidirect |
| 104. M16×C59 | D8 | semidirect |
| 201. #1980 | D59 | semidirect |
| 234. C59 | #10204 | semidirect |
| 311. M16 | #11745669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435403 | 2 |
| #21435214 | 2 |
| #21434555 | 2 |
| #21425048 | 2 |
| #21422590 | 2 |
| #21421947 | 2 |
| C59×#1980 | 2 |
| #10204 | 59 |