Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #21422166 | C2 | semidirect |
| 4. #21422151 | C2 | semidirect |
| 5. C59×#1713 | C2 | semidirect |
| 51. D472 | Q16 | semidirect |
| 86. #1713 | D59 | semidirect |
| 105. C59 | #12445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426230 | 2 |
| C8×D472 | 2 |
| #21422166 | 2 |
| #21422151 | 2 |
| C59×#1713 | 2 |
| #12445 | 59 |