Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20261218 | C2 | semidirect |
| 3. #20260741 | C2 | semidirect |
| 4. #20260637 | C2 | semidirect |
| 5. #20260503 | C2 | semidirect |
| 6. #20260495 | C2 | semidirect |
| 7. C2×#104×C97 | C2 | semidirect |
| 10. #15690835 | C4 | semidirect |
| 34. C2×D388 | C2×C4 | semidirect |
| 40. #13095495 | C2×C4 | semidirect |
| 75. Q8×C97 | C22⋊C4 | semidirect |
| 79. D4×C97 | C22⋊C4 | semidirect |
| 133. C97 | #1883 | semidirect |
| 136. C2×#104 | D97 | semidirect |
| 208. Q8 | #13095488 | semidirect |
| 216. D4 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690835 | 2 |
| #20261218 | 2 |
| #20260741 | 2 |
| #20260637 | 2 |
| #20260503 | 2 |
| #20260495 | 2 |
| C2×#104×C97 | 2 |
| #1883 | 97 |