Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
872 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 275 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. C2×Q8×Dic97 | C2 | semidirect |
| 3. #20260637 | C2 | semidirect |
| 4. #20260636 | C2 | semidirect |
| 5. #20260592 | C2 | semidirect |
| 6. C4×#13095488 | C2 | semidirect |
| 7. C2×C4×Q8×C97 | C2 | semidirect |
| 10. C2×#13095512 | C4 | semidirect |
| 57. Q8×C97 | C22⋊C4 | semidirect |
| 66. C2×C4×C97 | #41 | semidirect |
| 75. C2×Dic97 | #41 | semidirect |
| 107. C97 | #2341 | semidirect |
| 110. C2×C4×Q8 | D97 | semidirect |
| 164. Q8 | #13095488 | semidirect |
| 184. C2×C4 | #13095512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095512 | 2 |
| C2×Q8×Dic97 | 2 |
| #20260637 | 2 |
| #20260636 | 2 |
| #20260592 | 2 |
| C4×#13095488 | 2 |
| C2×C4×Q8×C97 | 2 |
| #2341 | 97 |