Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
540 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16837215 | C2 | semidirect |
| 4. #21425811 | C2 | semidirect |
| 5. #21424845 | C2 | semidirect |
| 6. #21422177 | C2 | semidirect |
| 7. C59×#2140 | C2 | semidirect |
| 61. #107×C59 | D4 | semidirect |
| 165. #2140 | D59 | semidirect |
| 191. C59 | #13413 | semidirect |
| 225. #107 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837777 | 2 |
| C2×#16837216 | 2 |
| C2×#16837215 | 2 |
| #21425811 | 2 |
| #21424845 | 2 |
| #21422177 | 2 |
| C59×#2140 | 2 |
| #13413 | 59 |