Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1318 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
|---|---|---|
| 1. C2×#16838014 | C2 | semidirect |
| 3. #21425242 | C2 | semidirect |
| 4. #21425178 | C2 | semidirect |
| 5. #21424454 | C2 | semidirect |
| 6. #21424408 | C2 | semidirect |
| 7. #21424167 | C2 | semidirect |
| 11. C2×#14273727 | C22 | semidirect |
| 13. C2×#14273719 | C22 | semidirect |
| 16. C2×C4×Dic118 | C22 | semidirect |
| 18. C2×#14273650 | C22 | semidirect |
| 21. #16837164 | C22 | semidirect |
| 22. #16837157 | C22 | semidirect |
| 23. #16837157 | C22 | semidirect |
| 217. C59 | #23942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838014 | 2 |
| C2×#16837553 | 2 |
| #21425242 | 2 |
| #21425178 | 2 |
| #21424454 | 2 |
| #21424408 | 2 |
| #21424167 | 2 |
| C59×#2309 | 2 |
| #23942 | 59 |