Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
462 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#16837216 | C2 | semidirect |
| 3. C2×#16837209 | C2 | semidirect |
| 4. C2×#16837202 | C2 | semidirect |
| 5. #21424879 | C2 | semidirect |
| 6. #21422186 | C2 | semidirect |
| 7. C59×#2139 | C2 | semidirect |
| 50. #14273663 | D4 | semidirect |
| 186. #2139 | D59 | semidirect |
| 216. C59 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434583 | 2 |
| C2×#16837216 | 2 |
| C2×#16837209 | 2 |
| C2×#16837202 | 2 |
| #21424879 | 2 |
| #21422186 | 2 |
| C59×#2139 | 2 |
| #13411 | 59 |