Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21432687 | C2 | semidirect |
| 3. #21425833 | C2 | semidirect |
| 4. C2×#16837211 | C2 | semidirect |
| 5. #21425725 | C2 | semidirect |
| 6. #21422210 | C2 | semidirect |
| 7. C59×#1383 | C2 | semidirect |
| 13. #16837678 | C4 | semidirect |
| 14. #16837673 | C4 | semidirect |
| 40. C2×Dic236 | C2×C4 | semidirect |
| 42. C2×D472 | C2×C4 | semidirect |
| 73. #108×C59 | C2×C4 | semidirect |
| 194. #1383 | D59 | semidirect |
| 222. C59 | #13005 | semidirect |
| 260. #108 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433817 | 2 |
| #21432687 | 2 |
| #21425833 | 2 |
| C2×#16837211 | 2 |
| #21425725 | 2 |
| #21422210 | 2 |
| C59×#1383 | 2 |
| #13005 | 59 |