Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
706 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 3. #21423713 | C2 | semidirect |
| 4. #21423705 | C2 | semidirect |
| 5. #21423691 | C2 | semidirect |
| 60. C2×C8×C59 | Q16 | semidirect |
| 136. C59 | #19604 | semidirect |
| 172. C2×C8 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434678 | 2 |
| #21434610 | 2 |
| #21423713 | 2 |
| #21423705 | 2 |
| #21423691 | 2 |
| C2×C8×C59⋊C8 | 2 |
| C59×#3160 | 2 |
| #19604 | 59 |