Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
270 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 97 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×#15690746 | C2 | semidirect |
| 3. #20260762 | C2 | semidirect |
| 5. #20260494 | C2 | semidirect |
| 6. #20260489 | C2 | semidirect |
| 23. #103×C97 | C4 | semidirect |
| 24. #103×C97 | C4 | semidirect |
| 25. #102×C97 | C4 | semidirect |
| 26. #102×C97 | C4 | semidirect |
| 110. C97 | #1866 | semidirect |
| 133. #103 | Dic97 | semidirect |
| 134. #103 | Dic97 | semidirect |
| 135. #102 | Dic97 | semidirect |
| 136. #102 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690817 | 2 |
| C2×#15690746 | 2 |
| #20260762 | 2 |
| C2×#15690737 | 2 |
| #20260494 | 2 |
| #20260489 | 2 |
| #416×C97 | 2 |
| #1866 | 97 |