Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
540 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 540 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×#16837214 | C2 | semidirect |
| 3. #21425813 | C2 | semidirect |
| 4. #21425812 | C2 | semidirect |
| 5. #21424842 | C2 | semidirect |
| 6. #21422177 | C2 | semidirect |
| 7. C2×C59×#361 | C2 | semidirect |
| 44. #14273661 | D4 | semidirect |
| 163. C2×#361 | D59 | semidirect |
| 191. C59 | #13413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837777 | 2 |
| C2×#16837214 | 2 |
| #21425813 | 2 |
| #21425812 | 2 |
| #21424842 | 2 |
| #21422177 | 2 |
| C2×C59×#361 | 2 |
| #13413 | 59 |