Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
588 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 210 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 |
|---|---|---|
| 19. #15690810 | C4 | semidirect |
| 20. #15690809 | C4 | semidirect |
| 21. #15690808 | C4 | semidirect |
| 24. C4⋊Q8×C97 | C4 | semidirect |
| 36. C4×#87604 | Q8 | semidirect |
| 84. #87604 | C4⋊Q8 | direct (N × H) |
| 87. C4×C97 | C4×Q8 | semidirect |
| 90. Dic97 | C4×Q8 | semidirect |
| 97. C97 | C4×C4⋊Q8 | semidirect |
| 109. C4⋊Q8 | #87604 | direct (N × H) |
| 187. C4 | Q8×#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 |
| (C2×#87604)⋊Q8 | 2 |
| #20261686 | 2 |
| #20261681 | 2 |
| C4⋊C4×#87604 | 2 |
| C42×#87604 | 2 |
| C4⋊Q8×D97 | 2 |
| C4×C4⋊Q8 | 97 |