Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 256 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. C2×#15690750 | C2 | semidirect |
| 2. C2×#15690746 | C2 | semidirect |
| 3. #20260548 | C2 | direct (N × H) |
| 7. #15690750 | C22 | semidirect |
| 10. #15690746 | C22 | semidirect |
| 76. C2×C97 | #361 | semidirect |
| 79. C97 | C2×#361 | semidirect |
| 155. C2 | #20260548 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690750 | 2 |
| C2×#15690746 | 2 |
| #20260548 | 2 |
| C22×D8×C97 | 2 |
| C2×#361 | 97 |