Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20261299 | C2 | semidirect |
| 2. C2×#15690806 | C2 | semidirect |
| 3. C2×#15690737 | C2 | semidirect |
| 4. #20260740 | C2 | semidirect |
| 5. C2×#15690726 | C2 | semidirect |
| 6. #20260496 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C97 | C2 | semidirect |
| 43. C4⋊Dic97 | D4 | semidirect |
| 48. C4×Dic97 | D4 | semidirect |
| 54. C2×Q8×C97 | D4 | semidirect |
| 61. C2×D4×C97 | D4 | semidirect |
| 62. C2×D4×C97 | D4 | semidirect |
| 68. M16×C97 | D4 | semidirect |
| 139. C97 | #2002 | semidirect |
| 140. C2×AGL(1,ℤ/8) | D97 | semidirect |
| 174. C2×Q8 | C22⋊D97 | semidirect |
| 190. C2×D4 | C22⋊D97 | semidirect |
| 191. C2×D4 | C22⋊D97 | semidirect |
| 200. M16 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261299 | 2 |
| C2×#15690806 | 2 |
| C2×#15690737 | 2 |
| #20260740 | 2 |
| C2×#15690726 | 2 |
| #20260496 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| #2002 | 97 |