Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
332 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 10. Q8×#87604 | C4 | semidirect |
| 17. #15690873 | C4 | semidirect |
| 23. #15690735 | C4 | semidirect |
| 24. #15690734 | C4 | semidirect |
| 25. #15690733 | C4 | semidirect |
| 26. #103×C97 | C4 | semidirect |
| 74. Q8×C97 | C42 | semidirect |
| 92. Dic194 | C42 | semidirect |
| 106. #87604 | #103 | direct (N × H) |
| 123. C97 | C4×#103 | semidirect |
| 147. #103 | #87604 | direct (N × H) |
| 189. 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 |
| C2×#15690873 | 2 |
| C2×C8×#87604 | 2 |
| C4⋊C4×#87604 | 2 |
| #20261609 | 2 |
| #20261608 | 2 |
| #103×D97 | 2 |
| C4×#103 | 97 |