Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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×#16837214 | C2 | semidirect |
| 4. #21425725 | C2 | semidirect |
| 5. #21424143 | C2 | semidirect |
| 6. #21422209 | C2 | semidirect |
| 7. C59×#2161 | C2 | semidirect |
| 159. #2161 | D59 | semidirect |
| 188. C59 | #13389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837673 | 2 |
| C2×#16837216 | 2 |
| C2×#16837214 | 2 |
| #21425725 | 2 |
| #21424143 | 2 |
| #21422209 | 2 |
| C59×#2161 | 2 |
| #13389 | 59 |