Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #21426413 | C2 | semidirect |
| 2. C2×#16837242 | C2 | semidirect |
| 3. #21426221 | C2 | semidirect |
| 4. #21422289 | C2 | semidirect |
| 5. #21422280 | C2 | semidirect |
| 6. #21422238 | C2 | semidirect |
| 141. C59 | #13672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426413 | 2 |
| C2×#16837242 | 2 |
| #21426221 | 2 |
| #21422289 | 2 |
| #21422280 | 2 |
| #21422238 | 2 |
| C59×#3417 | 2 |
| #13672 | 59 |