Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
340 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21437109 | C2 | semidirect |
| 3. #21426137 | C2 | semidirect |
| 4. #21423456 | C2 | semidirect |
| 5. #21422143 | C2 | semidirect |
| 6. #21422061 | C2 | semidirect |
| 7. C59×Q8⋊C16 | C2 | semidirect |
| 140. Q8⋊C16 | D59 | semidirect |
| 164. C59 | #12329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437109 | 2 |
| #21426346 | 2 |
| #21426137 | 2 |
| #21423456 | 2 |
| #21422143 | 2 |
| #21422061 | 2 |
| C59×Q8⋊C16 | 2 |
| #12329 | 59 |