Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20261049 | C2 | semidirect |
| 4. #20261046 | C2 | semidirect |
| 5. #20261028 | C2 | semidirect |
| 6. #20260933 | C2 | semidirect |
| 7. #20260874 | C2 | semidirect |
| 8. #20260838 | C2 | semidirect |
| 9. #20260836 | C2 | semidirect |
| 10. #20260789 | C2 | semidirect |
| 11. #448×C97 | C2 | semidirect |
| 87. Q8×C97 | #41 | semidirect |
| 141. C97 | #3112 | semidirect |
| 149. #448 | D97 | semidirect |
| 229. Q8 | #13095510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261280 | 2 |
| C2×Q8×Dic97 | 2 |
| #20261049 | 2 |
| #20261046 | 2 |
| #20261028 | 2 |
| #20260933 | 2 |
| #20260874 | 2 |
| #20260838 | 2 |
| #20260836 | 2 |
| #20260789 | 2 |
| #448×C97 | 2 |
| #3112 | 97 |