Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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×#15690767 | C2 | semidirect |
| 3. C2×C4⋊C4×D97 | C2 | semidirect |
| 4. #20260641 | C2 | semidirect |
| 5. #20260640 | C2 | semidirect |
| 6. #20260638 | C2 | semidirect |
| 7. #20260611 | C2 | semidirect |
| 8. #20260593 | C2 | semidirect |
| 9. #390×C97 | C2 | semidirect |
| 12. C2×#13095510 | C4 | semidirect |
| 36. C2×Dic194 | C2×C4 | semidirect |
| 42. C22×Dic97 | C2×C4 | semidirect |
| 61. C2×D4×C97 | C2×C4 | semidirect |
| 102. C4×D97 | C22⋊C4 | semidirect |
| 134. C97 | #2311 | semidirect |
| 141. #390 | D97 | semidirect |
| 177. C2×D4 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095510 | 2 |
| C2×#15690767 | 2 |
| C2×C4⋊C4×D97 | 2 |
| #20260641 | 2 |
| #20260640 | 2 |
| #20260638 | 2 |
| #20260611 | 2 |
| #20260593 | 2 |
| #390×C97 | 2 |
| #2311 | 97 |