Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15690721 | C2 | semidirect |
| 3. C4×C4⋊Dic97 | C2 | semidirect |
| 4. #20260497 | C2 | semidirect |
| 9. #15690731 | C4 | semidirect |
| 15. C4×D4×C97 | C4 | semidirect |
| 22. C2×#11715895 | C2×C4 | semidirect |
| 24. C4⋊Dic97 | C2×C4 | semidirect |
| 50. D4×C97 | C42 | semidirect |
| 91. C97 | #1762 | semidirect |
| 101. C4×D4 | Dic97 | semidirect |
| 141. D4 | C4×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690731 | 2 |
| C2×#15690721 | 2 |
| C4×C4⋊Dic97 | 2 |
| #20260497 | 2 |
| C2×C4×D4×C97 | 2 |
| #1762 | 97 |