Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
542 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21433119 | C2 | semidirect |
| 3. #21424103 | C2 | semidirect |
| 4. #21422495 | C2 | semidirect |
| 5. #21421992 | C2 | semidirect |
| 6. #21421954 | C2 | semidirect |
| 7. C59×#1517 | C2 | semidirect |
| 11. #16837604 | C4 | semidirect |
| 12. #16837594 | C4 | semidirect |
| 191. #1517 | D59 | semidirect |
| 221. C59 | #9305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433556 | 2 |
| #21433119 | 2 |
| #21424103 | 2 |
| #21422495 | 2 |
| #21421992 | 2 |
| #21421954 | 2 |
| C59×#1517 | 2 |
| #9305 | 59 |