Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
730 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21423788 | C2 | semidirect |
| 3. #21421921 | C2 | semidirect |
| 4. #21421917 | C2 | semidirect |
| 5. C59×#1270 | C2 | semidirect |
| 52. C2×D4×C59 | M16 | semidirect |
| 79. C2×Dic118 | M16 | semidirect |
| 170. #1270 | D59 | semidirect |
| 191. C59 | #7631 | semidirect |
| 234. C2×D4 | #11745659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426583 | 2 |
| #21423788 | 2 |
| #21421921 | 2 |
| #21421917 | 2 |
| C59×#1270 | 2 |
| #7631 | 59 |