Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4×#13095495 | C2 | semidirect |
| 3. C42×Dic97 | C2 | semidirect |
| 4. #20260494 | C2 | semidirect |
| 9. #15690737 | C4 | direct (N × H) |
| 13. C4×Q8×C97 | C4 | semidirect |
| 15. C4×D4×C97 | C4 | semidirect |
| 22. #13095495 | C2×C4 | semidirect |
| 26. C4×Dic97 | C2×C4 | semidirect |
| 48. Q8×C97 | C42 | semidirect |
| 51. D4×C97 | C42 | semidirect |
| 74. C4×C97 | #104 | semidirect |
| 84. C97 | C4×#104 | semidirect |
| 92. C4×Q8 | Dic97 | semidirect |
| 94. C4×D4 | Dic97 | semidirect |
| 132. Q8 | C4×Dic97 | semidirect |
| 135. D4 | C4×Dic97 | semidirect |
| 159. C4 | #15690737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690737 | 2 |
| C4×#13095495 | 2 |
| C42×Dic97 | 2 |
| #20260494 | 2 |
| C4×#41×C97 | 2 |
| C4×#104 | 97 |