Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
462 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16837210 | C2 | semidirect |
| 4. #21425809 | C2 | semidirect |
| 5. C2×#16837204 | C2 | semidirect |
| 6. #21424881 | C2 | semidirect |
| 7. C59×#1379 | C2 | semidirect |
| 54. #14273663 | D4 | semidirect |
| 189. #1379 | D59 | semidirect |
| 216. C59 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434582 | 2 |
| C2×#16837216 | 2 |
| C2×#16837210 | 2 |
| #21425809 | 2 |
| C2×#16837204 | 2 |
| #21424881 | 2 |
| C59×#1379 | 2 |
| #13411 | 59 |