Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20261131 | C2 | semidirect |
| 3. #20261109 | C2 | semidirect |
| 4. #20261085 | C2 | semidirect |
| 5. #20261083 | C2 | semidirect |
| 6. #20260966 | C2 | semidirect |
| 7. C4×#13095498 | C2 | semidirect |
| 8. C2×C4×#11715895 | C2 | semidirect |
| 9. #533×C97 | C2 | semidirect |
| 75. C2×C4×C97 | SD16 | semidirect |
| 90. #11715895 | #41 | semidirect |
| 113. C97 | #3167 | semidirect |
| 114. #533 | D97 | semidirect |
| 195. C2×C4 | #13095498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261285 | 2 |
| #20261131 | 2 |
| #20261109 | 2 |
| #20261085 | 2 |
| #20261083 | 2 |
| #20260966 | 2 |
| C4×#13095498 | 2 |
| C2×C4×#11715895 | 2 |
| #533×C97 | 2 |
| #3167 | 97 |