Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21422706 | C2 | semidirect |
| 3. #21422530 | C2 | semidirect |
| 4. #21422514 | C2 | semidirect |
| 5. #21421995 | C2 | semidirect |
| 6. #21421968 | C2 | semidirect |
| 7. C59×#2923 | C2 | semidirect |
| 185. #2923 | D59 | semidirect |
| 220. C59 | #9313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434247 | 2 |
| #21422706 | 2 |
| #21422530 | 2 |
| #21422514 | 2 |
| #21421995 | 2 |
| #21421968 | 2 |
| C59×#2923 | 2 |
| #9313 | 59 |