Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
628 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 290 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 |
|---|---|---|
| 6. Q8×#87604 | C4 | semidirect |
| 14. Q8×Dic97 | C4 | semidirect |
| 15. C4×Dic194 | C4 | semidirect |
| 16. #15690775 | C4 | semidirect |
| 19. C4×Q8×C97 | C4 | semidirect |
| 45. Q8×C97 | C42 | semidirect |
| 56. Dic194 | C42 | semidirect |
| 76. C97 | #2276 | semidirect |
| 87. C4×Q8 | #87604 | semidirect |
| 116. Q8 | C4×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#87604 | 2 |
| C4⋊C4×#87604 | 2 |
| C4×C4⋊#87604 | 2 |
| #20261671 | 2 |
| C4×Q8×D97 | 2 |
| #2276 | 97 |