Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20260595 | C2 | semidirect |
| 3. #20260502 | C2 | semidirect |
| 10. C23×C4×C97 | C4 | semidirect |
| 14. C2×C4⋊C4×C97 | C4 | semidirect |
| 15. C2×C22⋊C4×C97 | C4 | semidirect |
| 17. C2×C42×C97 | C4 | semidirect |
| 50. C23×C97 | C4⋊C4 | semidirect |
| 73. C2×C4×C97 | C4⋊C4 | semidirect |
| 99. C4×C97 | #99 | semidirect |
| 110. C97 | #1799 | semidirect |
| 116. C23×C4 | Dic97 | semidirect |
| 121. C2×C4⋊C4 | Dic97 | semidirect |
| 123. C2×C22⋊C4 | Dic97 | semidirect |
| 125. C2×C42 | Dic97 | semidirect |
| 160. C23 | C4⋊Dic97 | semidirect |
| 186. C2×C4 | C4⋊Dic97 | semidirect |
| 210. C4 | #15690725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690725 | 2 |
| #20260595 | 2 |
| #20260502 | 2 |
| C2×C4×D4×C97 | 2 |
| #1799 | 97 |