Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
544 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 181 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×#15690810 | C2 | semidirect |
| 3. #20260940 | C2 | direct (N × H) |
| 4. C2×C4⋊#11715895 | C2 | semidirect |
| 5. C2×#15690733 | C2 | semidirect |
| 12. #15690810 | C22 | semidirect |
| 15. C4⋊#11715895 | C22 | semidirect |
| 16. #15690733 | C22 | semidirect |
| 62. C2×C4×C97 | SD16 | semidirect |
| 86. C4×C97 | C2×SD16 | semidirect |
| 91. C2×C97 | #461 | semidirect |
| 96. C97 | C2×#461 | semidirect |
| 163. C2×C4 | #13095499 | semidirect |
| 183. C4 | C2×#13095499 | semidirect |
| 187. C2 | #20260940 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095499 | 2 |
| C2×#15690810 | 2 |
| #20260940 | 2 |
| C2×C4⋊#11715895 | 2 |
| C2×#15690733 | 2 |
| C2×C4×D4×C97 | 2 |
| C2×#461 | 97 |