Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
454 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21425845 | C2 | semidirect |
| 3. C2×#16837216 | C2 | semidirect |
| 4. C2×#16837214 | C2 | semidirect |
| 5. #21424887 | C2 | semidirect |
| 6. #21422183 | C2 | semidirect |
| 7. C59×#2143 | C2 | semidirect |
| 67. #108×C59 | D4 | semidirect |
| 173. #2143 | D59 | semidirect |
| 201. C59 | #13417 | semidirect |
| 240. #108 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434583 | 2 |
| #21425845 | 2 |
| C2×#16837216 | 2 |
| C2×#16837214 | 2 |
| #21424887 | 2 |
| #21422183 | 2 |
| C59×#2143 | 2 |
| #13417 | 59 |