Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1072 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 175 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. #21434645 | C2 | semidirect |
| 3. #21433914 | C2 | semidirect |
| 4. #21425306 | C2 | semidirect |
| 5. #21425077 | C2 | semidirect |
| 6. #21424937 | C2 | semidirect |
| 7. #21424305 | C2 | semidirect |
| 8. #21423907 | C2 | semidirect |
| 9. C59×#2641 | C2 | semidirect |
| 137. #11745664 | #41 | semidirect |
| 198. #2641 | D59 | semidirect |
| 236. C59 | #25690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437970 | 2 |
| #21434645 | 2 |
| #21433914 | 2 |
| #21425306 | 2 |
| #21425077 | 2 |
| #21424937 | 2 |
| #21424305 | 2 |
| #21423907 | 2 |
| C59×#2641 | 2 |
| #25690 | 59 |