Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21425811 | C2 | semidirect |
| 4. #21422178 | C2 | semidirect |
| 5. C59×#1945 | C2 | semidirect |
| 40. #107×C59 | D4 | semidirect |
| 117. #1945 | D59 | semidirect |
| 136. C59 | #13413 | semidirect |
| 159. #107 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837779 | 2 |
| C2×#16837214 | 2 |
| #21425811 | 2 |
| #21422178 | 2 |
| C59×#1945 | 2 |
| #13413 | 59 |