Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20260639 | C2 | semidirect |
| 3. #20260626 | C2 | semidirect |
| 4. #20260625 | C2 | semidirect |
| 6. #20260606 | C2 | semidirect |
| 7. #20260603 | C2 | semidirect |
| 8. C4×#13095488 | C2 | semidirect |
| 9. C4×C4⋊C4×C97 | C2 | semidirect |
| 13. #15690798 | C4 | semidirect |
| 34. C2×Dic194 | C2×C4 | semidirect |
| 47. #13095488 | C2×C4 | semidirect |
| 48. #13095488 | C2×C4 | semidirect |
| 58. C42×C97 | C2×C4 | semidirect |
| 119. C97 | #2337 | semidirect |
| 127. C4×C4⋊C4 | D97 | semidirect |
| 177. C42 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690798 | 2 |
| #20260639 | 2 |
| #20260626 | 2 |
| #20260625 | 2 |
| #20260613 | 2 |
| #20260606 | 2 |
| #20260603 | 2 |
| C4×#13095488 | 2 |
| C4×C4⋊C4×C97 | 2 |
| #2337 | 97 |