Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1252 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 261 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. C22×#13095488 | C2 | semidirect |
| 3. C22×#13095488 | C2 | semidirect |
| 4. #20260652 | C2 | direct (N × H) |
| 5. C2×#15690717 | C2 | semidirect |
| 6. C22×C4⋊C4×C97 | C2 | semidirect |
| 14. C2×#13095488 | C22 | semidirect |
| 15. C2×#13095488 | C22 | semidirect |
| 16. #15690717 | C22 | semidirect |
| 21. C2×C4⋊C4×C97 | C22 | semidirect |
| 46. C22×C4×C97 | D4 | semidirect |
| 80. C2×C4×C97 | C2×D4 | semidirect |
| 108. C2×C97 | #394 | semidirect |
| 116. C97 | C2×#394 | semidirect |
| 118. C22×C4⋊C4 | D97 | semidirect |
| 132. C2×C4⋊C4 | C2×D97 | semidirect |
| 159. C22×C4 | D388 | semidirect |
| 201. C2×C4 | C2×D388 | semidirect |
| 225. C2 | #20260652 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D388 | 2 |
| C22×#13095488 | 2 |
| #20260652 | 2 |
| C2×#15690717 | 2 |
| C22×C4⋊C4×C97 | 2 |
| C2×#394 | 97 |