Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
412 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21425907 | C2 | semidirect |
| 3. #21422137 | C2 | semidirect |
| 4. #21422132 | C2 | semidirect |
| 5. C59×#1359 | C2 | semidirect |
| 14. #16837223 | C22 | semidirect |
| 18. C59×#364 | C22 | semidirect |
| 124. #1359 | D59 | semidirect |
| 142. #364 | C2×D59 | semidirect |
| 145. C59 | #11992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434543 | 2 |
| #21425907 | 2 |
| #21422137 | 2 |
| #21422132 | 2 |
| C59×#1359 | 2 |
| #11992 | 59 |