Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
334 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 68 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. #20261728 | C2 | semidirect |
| 4. (C2×#87604)⋊Q8 | C2 | semidirect |
| 5. #20261614 | C2 | semidirect |
| 6. #20261607 | C2 | semidirect |
| 24. #15690843 | C4 | semidirect |
| 26. #15690841 | C4 | semidirect |
| 27. #15690840 | C4 | semidirect |
| 32. #137×C97 | C4 | semidirect |
| 56. C2×Dic194 | C2×C4 | semidirect |
| 73. #13095495 | C2×C4 | semidirect |
| 77. C2×Q8×C97 | C2×C4 | semidirect |
| 80. M16×C97 | C2×C4 | semidirect |
| 154. C97 | #1882 | semidirect |
| 169. #137 | #87604 | semidirect |
| 200. C2×Q8 | C2×#87604 | semidirect |
| 221. M16 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261804 | 2 |
| D97⋊#104 | 2 |
| #20261728 | 2 |
| (C2×#87604)⋊Q8 | 2 |
| #20261614 | 2 |
| #20261607 | 2 |
| #137×D97 | 2 |
| #1882 | 97 |