Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
538 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16837513 | C2 | semidirect |
| 3. C2×#16837214 | C2 | semidirect |
| 4. C2×#16837211 | C2 | semidirect |
| 5. #21424987 | C2 | semidirect |
| 6. #21422175 | C2 | semidirect |
| 7. C59×#1383 | C2 | semidirect |
| 13. C2×#14273672 | C4 | semidirect |
| 14. C2×D944 | C4 | semidirect |
| 34. C2×Dic236 | C2×C4 | semidirect |
| 40. C2×D472 | C2×C4 | semidirect |
| 63. C2×C16×C59 | C2×C4 | semidirect |
| 178. #1383 | D59 | semidirect |
| 205. C59 | #13037 | semidirect |
| 237. C2×C16 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837840 | 2 |
| C2×#16837513 | 2 |
| C2×#16837214 | 2 |
| C2×#16837211 | 2 |
| #21424987 | 2 |
| #21422175 | 2 |
| C59×#1383 | 2 |
| #13037 | 59 |