Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×Dic194 | C2 | semidirect |
| 3. #20261081 | C2 | semidirect |
| 4. #20261080 | C2 | semidirect |
| 5. #20261026 | C2 | semidirect |
| 6. #20261023 | C2 | semidirect |
| 7. #20260933 | C2 | semidirect |
| 8. #20260859 | C2 | semidirect |
| 9. SD16×Dic97 | C2 | semidirect |
| 10. C4×#13095498 | C2 | semidirect |
| 11. #460×C97 | C2 | semidirect |
| 77. Q8×C97 | #41 | semidirect |
| 99. Dic194 | SD16 | semidirect |
| 126. C97 | #3362 | semidirect |
| 134. #460 | D97 | semidirect |
| 206. Q8 | #13095510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic194 | 2 |
| #20261405 | 2 |
| #20261081 | 2 |
| #20261080 | 2 |
| #20261026 | 2 |
| #20261023 | 2 |
| #20260933 | 2 |
| #20260859 | 2 |
| SD16×Dic97 | 2 |
| C4×#13095498 | 2 |
| #460×C97 | 2 |
| #3362 | 97 |