Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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×#15690737 | C2 | semidirect |
| 3. #20260739 | C2 | semidirect |
| 4. #20260636 | C2 | semidirect |
| 5. #20260504 | C2 | semidirect |
| 6. #20260494 | C2 | semidirect |
| 7. #520×C97 | C2 | semidirect |
| 10. #15690835 | C4 | semidirect |
| 34. C2×D388 | C2×C4 | semidirect |
| 41. #13095495 | C2×C4 | semidirect |
| 75. Q8×C97 | C22⋊C4 | semidirect |
| 79. D4×C97 | C22⋊C4 | semidirect |
| 133. C97 | #1883 | semidirect |
| 135. #520 | 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 |
| C2×#15690737 | 2 |
| #20260739 | 2 |
| #20260636 | 2 |
| #20260504 | 2 |
| #20260494 | 2 |
| #520×C97 | 2 |
| #1883 | 97 |