Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
336 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 61 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. #21426264 | C2 | semidirect |
| 3. #21423730 | C2 | semidirect |
| 4. #21422134 | C2 | semidirect |
| 5. #21422072 | C2 | semidirect |
| 6. #21422071 | C2 | semidirect |
| 7. C59×#2230 | C2 | semidirect |
| 160. #2230 | D59 | semidirect |
| 188. C59 | #12367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435901 | 2 |
| #21426264 | 2 |
| #21423730 | 2 |
| #21422134 | 2 |
| #21422072 | 2 |
| #21422071 | 2 |
| C59×#2230 | 2 |
| #12367 | 59 |