Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
296 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 13. #15690729 | C4 | semidirect |
| 18. #101×C97 | C4 | semidirect |
| 70. Dic97 | #101 | direct (N × H) |
| 77. C97 | C4×#101 | semidirect |
| 93. #101 | Dic97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic97 | 2 |
| C2×#15690729 | 2 |
| M16×Dic97 | 2 |
| #20260503 | 2 |
| C2×#101×C97 | 2 |
| C4×#101 | 97 |