Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. C2×#15690750 | C2 | semidirect |
| 2. #20260773 | C2 | semidirect |
| 3. #20260545 | C2 | semidirect |
| 7. #15690750 | C22 | semidirect |
| 10. #15690742 | C22 | semidirect |
| 14. #135×C97 | C4 | semidirect |
| 16. C2×Q16×C97 | C4 | semidirect |
| 18. C2×D8×C97 | C4 | semidirect |
| 85. C97 | #2145 | semidirect |
| 93. #135 | Dic97 | semidirect |
| 95. C2×Q16 | Dic97 | semidirect |
| 97. C2×D8 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690750 | 2 |
| #20260773 | 2 |
| #20260545 | 2 |
| C2×#135×C97 | 2 |
| #2145 | 97 |