Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 217 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. Q8×#11715895 | C2 | semidirect |
| 3. C8×Dic194 | C2 | semidirect |
| 4. #20260859 | C2 | semidirect |
| 7. C8×Q8×C97 | C2 | semidirect |
| 25. Q8×D97 | C8 | semidirect |
| 74. C97 | #2982 | semidirect |
| 79. C8×Q8 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D97 | 2 |
| Q8×#11715895 | 2 |
| C8×Dic194 | 2 |
| #20260859 | 2 |
| #20260787 | 2 |
| #20260786 | 2 |
| C8×Q8×C97 | 2 |
| #2982 | 97 |