Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
332 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 11. #15690775 | C4 | semidirect |
| 17. #15690735 | C4 | semidirect |
| 18. #15690733 | C4 | semidirect |
| 82. Dic194 | C42 | semidirect |
| 101. Dic97 | #103 | semidirect |
| 110. C97 | C4×#103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690775 | 2 |
| C2×#15690735 | 2 |
| C2×#15690733 | 2 |
| C2×C8×Dic97 | 2 |
| C4⋊C4×Dic97 | 2 |
| #20260497 | 2 |
| #340×C97 | 2 |
| C4×#103 | 97 |