Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. #20261739 | C2 | semidirect |
| 3. C4×C4⋊#87604 | C2 | semidirect |
| 4. #20261605 | C2 | semidirect |
| 14. Q8×Dic97 | C4 | semidirect |
| 16. C4×D388 | C4 | semidirect |
| 18. #15690772 | C4 | semidirect |
| 23. C4×Q8×C97 | C4 | semidirect |
| 64. Q8×C97 | C4⋊C4 | semidirect |
| 77. D388 | C4⋊C4 | semidirect |
| 101. C4×C97 | #104 | semidirect |
| 116. C97 | #1806 | semidirect |
| 125. C4×Q8 | #87604 | semidirect |
| 177. Q8 | C4⋊#87604 | semidirect |
| 222. C4 | #15690875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261739 | 2 |
| C2×#15690875 | 2 |
| C4×C4⋊#87604 | 2 |
| #20261605 | 2 |
| C4×#13095512 | 2 |
| #1806 | 97 |