Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
480 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 3. #20260843 | C2 | semidirect |
| 4. #20260842 | C2 | semidirect |
| 5. #20260841 | C2 | semidirect |
| 6. #20260840 | C2 | semidirect |
| 7. #20260839 | C2 | semidirect |
| 11. #441×C97 | C2 | semidirect |
| 15. Q16×D97 | C4 | semidirect |
| 48. Dic388 | C2×C4 | semidirect |
| 49. #13095501 | C2×C4 | semidirect |
| 65. Q16×C97 | C2×C4 | semidirect |
| 109. D97 | #441 | direct (N × H) |
| 111. C97 | C2×#441 | semidirect |
| 119. #441 | D97 | direct (N × H) |
| 162. Q16 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D97 | 2 |
| C4×Q8×D97 | 2 |
| #20260843 | 2 |
| #20260842 | 2 |
| #20260841 | 2 |
| #20260840 | 2 |
| #20260839 | 2 |
| #106×D97 | 2 |
| #103×D97 | 2 |
| #97×D97 | 2 |
| #441×C97 | 2 |
| C2×#441 | 97 |