Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20261311 | C2 | semidirect |
| 3. C2×#15690798 | C2 | semidirect |
| 4. C2×#15690738 | C2 | semidirect |
| 5. #20260739 | C2 | semidirect |
| 6. C2×#15690728 | C2 | semidirect |
| 7. #339×C97 | C2 | semidirect |
| 131. C97 | #2003 | semidirect |
| 138. #339 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690838 | 2 |
| #20261311 | 2 |
| C2×#15690798 | 2 |
| C2×#15690738 | 2 |
| #20260739 | 2 |
| C2×#15690728 | 2 |
| #339×C97 | 2 |
| #2003 | 97 |