Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
390 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 74 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×#13095520 | C2 | semidirect |
| 2. C2×#15690870 | C2 | semidirect |
| 3. #20261705 | C2 | semidirect |
| 4. #20261615 | C2 | semidirect |
| 29. #13095520 | D4 | semidirect |
| 114. C22×C97 | #100 | semidirect |
| 137. C97 | #1900 | semidirect |
| 255. C22 | #15690870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095520 | 2 |
| C2×#15690870 | 2 |
| #20261705 | 2 |
| #20261615 | 2 |
| C2×#15690782 | 2 |
| #1900 | 97 |