Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21433013 | C2 | semidirect |
| 3. C2×#16837216 | C2 | semidirect |
| 4. #21425004 | C2 | semidirect |
| 5. #21422199 | C2 | semidirect |
| 6. #21422183 | C2 | semidirect |
| 7. C59×#2143 | C2 | semidirect |
| 12. C2×#14273670 | C4 | semidirect |
| 13. C2×#14273668 | C4 | semidirect |
| 168. #2143 | D59 | semidirect |
| 197. C59 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837837 | 2 |
| #21433013 | 2 |
| C2×#16837216 | 2 |
| #21425004 | 2 |
| #21422199 | 2 |
| #21422183 | 2 |
| C59×#2143 | 2 |
| #13036 | 59 |