Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
474 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×#13095500 | C2 | semidirect |
| 2. C22×#13095499 | C2 | semidirect |
| 4. C2×#15690730 | C2 | semidirect |
| 5. #20260640 | C2 | semidirect |
| 6. #20260489 | C2 | semidirect |
| 7. C2×#102×C97 | C2 | semidirect |
| 33. C2×Dic194 | D4 | semidirect |
| 49. C2×#11715895 | D4 | semidirect |
| 63. C2×C8×C97 | D4 | semidirect |
| 95. C2×Dic97 | SD16 | semidirect |
| 136. C97 | #2014 | semidirect |
| 141. C2×#102 | D97 | semidirect |
| 197. C2×C8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095500 | 2 |
| C22×#13095499 | 2 |
| C2×#15690806 | 2 |
| C2×#15690730 | 2 |
| #20260640 | 2 |
| #20260489 | 2 |
| C2×#102×C97 | 2 |
| #2014 | 97 |