Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 2. C2×#16837241 | C2 | semidirect |
| 3. #21426187 | C2 | semidirect |
| 4. #21422275 | C2 | semidirect |
| 5. C59×C22⋊C32 | C2 | semidirect |
| 7. C2×Dic472 | C22 | semidirect |
| 13. #16837228 | C22 | semidirect |
| 16. C2×C32×C59 | C22 | semidirect |
| 78. C22×C59 | SD64 | semidirect |
| 93. C22⋊C32 | D59 | semidirect |
| 107. C2×C32 | C2×D59 | semidirect |
| 110. C59 | #13664 | semidirect |
| 175. C22 | #16837241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D944 | 2 |
| C2×#16837241 | 2 |
| #21426187 | 2 |
| #21422275 | 2 |
| C59×C22⋊C32 | 2 |
| #13664 | 59 |