Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
318 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 57 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. #21426293 | C2 | semidirect |
| 3. #21425537 | C2 | semidirect |
| 4. #21422115 | C2 | semidirect |
| 5. #21422111 | C2 | semidirect |
| 6. #21422021 | C2 | semidirect |
| 7. C59×#2233 | C2 | semidirect |
| 153. #2233 | D59 | semidirect |
| 183. C59 | #12285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434992 | 2 |
| #21426293 | 2 |
| #21425537 | 2 |
| #21422115 | 2 |
| #21422111 | 2 |
| #21422021 | 2 |
| C59×#2233 | 2 |
| #12285 | 59 |