Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 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. #20261210 | C2 | semidirect |
| 3. #20261209 | C2 | semidirect |
| 4. #20260844 | C2 | semidirect |
| 5. #20260815 | C2 | semidirect |
| 6. #20260771 | C2 | semidirect |
| 7. #20260741 | C2 | semidirect |
| 8. #20260693 | C2 | semidirect |
| 9. #418×C97 | C2 | semidirect |
| 11. C2×#13095496 | C4 | semidirect |
| 17. D4×Dic97 | C22 | semidirect |
| 18. #15690772 | C22 | semidirect |
| 23. #15690743 | C22 | semidirect |
| 24. #15690741 | C22 | semidirect |
| 25. #15690732 | C22 | semidirect |
| 26. #15690720 | C22 | semidirect |
| 27. C8×Dic97 | C22 | semidirect |
| 31. #102×C97 | C22 | semidirect |
| 35. C2×D388 | C2×C4 | semidirect |
| 39. #13095496 | C2×C4 | semidirect |
| 40. #13095496 | C2×C4 | semidirect |
| 41. C2×#11715895 | C2×C4 | semidirect |
| 55. C2×D4×C97 | C2×C4 | semidirect |
| 109. C97 | #2948 | semidirect |
| 117. #418 | D97 | semidirect |
| 138. #102 | C2×D97 | semidirect |
| 149. 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×#13095496 | 2 |
| #20261210 | 2 |
| #20261209 | 2 |
| #20260844 | 2 |
| #20260815 | 2 |
| #20260771 | 2 |
| #20260741 | 2 |
| #20260693 | 2 |
| #418×C97 | 2 |
| #2948 | 97 |