Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
496 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 91 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×#13095496 | C2 | semidirect |
| 2. C2×#15690785 | C2 | semidirect |
| 3. C2×#15690781 | C2 | semidirect |
| 4. C2×#15690732 | C2 | semidirect |
| 5. C2×#15690722 | C2 | semidirect |
| 6. #20260497 | C2 | semidirect |
| 7. C2×#102×C97 | C2 | semidirect |
| 39. C2×D388 | D4 | semidirect |
| 54. C2×#11715895 | D4 | semidirect |
| 56. C4⋊Dic97 | D4 | semidirect |
| 65. C2×D4×C97 | D4 | semidirect |
| 72. C4⋊C4×C97 | D4 | semidirect |
| 94. C22×D97 | D8 | semidirect |
| 172. C97 | #1999 | semidirect |
| 177. C2×#102 | D97 | semidirect |
| 221. C2×D4 | D388 | semidirect |
| 242. C4⋊C4 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095496 | 2 |
| C2×#15690785 | 2 |
| C2×#15690781 | 2 |
| C2×#15690732 | 2 |
| C2×#15690722 | 2 |
| #20260497 | 2 |
| C2×#102×C97 | 2 |
| #1999 | 97 |