Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 166 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×#15690898 | C2 | semidirect |
| 2. #20261769 | C2 | semidirect |
| 3. #20261765 | C2 | semidirect |
| 4. #20261763 | C2 | semidirect |
| 5. #20261736 | C2 | semidirect |
| 6. #20261710 | C2 | semidirect |
| 7. C4×#13095521 | C2 | semidirect |
| 33. #13095521 | D4 | semidirect |
| 93. C4×C97 | #131 | semidirect |
| 104. C97 | #2935 | semidirect |
| 201. C4 | #15690898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690898 | 2 |
| #20261769 | 2 |
| #20261765 | 2 |
| #20261763 | 2 |
| #20261736 | 2 |
| #20261710 | 2 |
| C4×#13095521 | 2 |
| #20261286 | 2 |
| #2935 | 97 |