Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20261535 | C2 | semidirect |
| 2. C2×#15690838 | C2 | semidirect |
| 3. #20261304 | C2 | semidirect |
| 4. #20260751 | C2 | semidirect |
| 5. #20260741 | C2 | semidirect |
| 6. #20260708 | C2 | semidirect |
| 7. #344×C97 | C2 | semidirect |
| 41. C2×Dic194 | D4 | semidirect |
| 50. C2×D388 | D4 | semidirect |
| 69. M16×C97 | D4 | semidirect |
| 71. C2×C8×C97 | D4 | semidirect |
| 143. C97 | #2008 | semidirect |
| 150. #344 | D97 | semidirect |
| 208. M16 | D388 | semidirect |
| 210. C2×C8 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261535 | 2 |
| C2×#15690838 | 2 |
| #20261304 | 2 |
| #20260751 | 2 |
| #20260741 | 2 |
| #20260708 | 2 |
| #344×C97 | 2 |
| #2008 | 97 |