Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
360 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21425908 | C2 | semidirect |
| 2. #21422399 | C2 | semidirect |
| 3. #21422072 | C2 | semidirect |
| 4. #21422069 | C2 | semidirect |
| 7. #16837223 | C22 | semidirect |
| 11. #16837123 | C22 | semidirect |
| 12. C8×C59⋊C8 | C22 | semidirect |
| 59. Q16×C59 | M16 | semidirect |
| 63. D8×C59 | M16 | semidirect |
| 146. C59 | #11669 | semidirect |
| 184. Q16 | #11745664 | semidirect |
| 188. D8 | #11745664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425908 | 2 |
| #21422399 | 2 |
| #21422072 | 2 |
| #21422069 | 2 |
| C59×#2956 | 2 |
| #11669 | 59 |