Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 99 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×#15690743 | C2 | semidirect |
| 3. C2×#15690734 | C2 | semidirect |
| 5. C2×#15690721 | C2 | semidirect |
| 7. #391×C97 | C2 | semidirect |
| 11. C2×#13095498 | C4 | semidirect |
| 87. #11715895 | C22⋊C4 | semidirect |
| 113. C97 | #1973 | semidirect |
| 119. #391 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095498 | 2 |
| C2×#15690743 | 2 |
| C2×#15690734 | 2 |
| C2×#15690730 | 2 |
| C2×#15690721 | 2 |
| #20260637 | 2 |
| #391×C97 | 2 |
| #1973 | 97 |