Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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. C22×C4⋊#87604 | C2 | semidirect |
| 2. C2×#15690872 | C2 | semidirect |
| 3. #20261703 | C2 | semidirect |
| 4. #20261608 | C2 | semidirect |
| 17. #15690785 | C4 | semidirect |
| 18. #15690784 | C4 | semidirect |
| 21. #15690781 | C4 | semidirect |
| 24. #121×C97 | C4 | semidirect |
| 34. C4⋊#87604 | D4 | semidirect |
| 38. C2×D388 | C2×C4 | semidirect |
| 54. C4⋊Dic97 | C2×C4 | semidirect |
| 60. C2×D4×C97 | C2×C4 | semidirect |
| 62. C4⋊C4×C97 | C2×C4 | semidirect |
| 114. C22×C97 | #102 | semidirect |
| 129. C2×D97 | #102 | semidirect |
| 155. C97 | #1874 | semidirect |
| 171. #121 | #87604 | semidirect |
| 192. C2×D4 | C2×#87604 | semidirect |
| 214. C4⋊C4 | C2×#87604 | semidirect |
| 289. C22 | #15690872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#87604 | 2 |
| C2×#15690872 | 2 |
| #20261703 | 2 |
| #20261608 | 2 |
| #121×D97 | 2 |
| #1874 | 97 |