Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20261085 | C2 | semidirect |
| 3. #20261063 | C2 | semidirect |
| 4. #20261020 | C2 | semidirect |
| 5. #20260966 | C2 | semidirect |
| 6. #20260937 | C2 | semidirect |
| 7. #20260874 | C2 | semidirect |
| 8. C4×#13095498 | C2 | semidirect |
| 9. D4×#11715895 | C2 | semidirect |
| 10. C2×#15690734 | C2 | semidirect |
| 11. D4×Q8×C97 | C2 | semidirect |
| 83. Q8×C97 | #41 | semidirect |
| 84. D4×C97 | SD16 | semidirect |
| 129. C97 | #3298 | semidirect |
| 130. D4×Q8 | D97 | semidirect |
| 213. Q8 | #13095510 | semidirect |
| 217. D4 | #13095498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261389 | 2 |
| #20261085 | 2 |
| #20261063 | 2 |
| #20261020 | 2 |
| #20260966 | 2 |
| #20260937 | 2 |
| #20260874 | 2 |
| C4×#13095498 | 2 |
| D4×#11715895 | 2 |
| C2×#15690734 | 2 |
| D4×Q8×C97 | 2 |
| #3298 | 97 |