Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21426376 | C2 | semidirect |
| 3. #21423487 | C2 | semidirect |
| 4. #21422153 | C2 | semidirect |
| 5. #21422074 | C2 | semidirect |
| 59. D8×C59 | Q16 | semidirect |
| 147. C59 | #12407 | semidirect |
| 183. D8 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436961 | 2 |
| #21426376 | 2 |
| #21423487 | 2 |
| #21422153 | 2 |
| #21422074 | 2 |
| #21422057 | 2 |
| C59×#2224 | 2 |
| #12407 | 59 |