Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20261502 | C2 | semidirect |
| 2. #20260752 | C2 | semidirect |
| 3. #20260731 | C2 | semidirect |
| 4. #20260702 | C2 | semidirect |
| 5. #20260507 | C2 | semidirect |
| 6. #20260499 | C2 | semidirect |
| 22. #137×C97 | C4 | semidirect |
| 24. AGL(1,ℤ/8)×C97 | C4 | semidirect |
| 119. C97 | #1881 | semidirect |
| 130. #137 | Dic97 | semidirect |
| 132. AGL(1,ℤ/8) | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261502 | 2 |
| #20260752 | 2 |
| #20260731 | 2 |
| #20260702 | 2 |
| #20260507 | 2 |
| #20260499 | 2 |
| #575×C97 | 2 |
| #1881 | 97 |