Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
618 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 129 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×#15690737 | C2 | semidirect |
| 2. #20260699 | C2 | semidirect |
| 3. C4×C22⋊Dic97 | C2 | semidirect |
| 5. C2×#13095495 | C22 | semidirect |
| 7. C2×C4×Dic97 | C22 | semidirect |
| 15. C2×#41×C97 | C4 | semidirect |
| 17. C22×Q8×C97 | C4 | semidirect |
| 19. C22×D4×C97 | C4 | semidirect |
| 67. Q8×C97 | C22⋊C4 | semidirect |
| 72. D4×C97 | C22⋊C4 | semidirect |
| 103. C22×C97 | #104 | semidirect |
| 120. C97 | #1789 | semidirect |
| 128. C2×#41 | Dic97 | semidirect |
| 130. C22×Q8 | Dic97 | semidirect |
| 132. C22×D4 | Dic97 | semidirect |
| 187. Q8 | C22⋊Dic97 | semidirect |
| 192. D4 | C22⋊Dic97 | semidirect |
| 223. C22 | #15690737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690737 | 2 |
| #20260699 | 2 |
| C4×C22⋊Dic97 | 2 |
| C22×#41×C97 | 2 |
| #1789 | 97 |