Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
192 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 71 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. D4×#11715895 | C2 | semidirect |
| 3. #20260800 | C2 | semidirect |
| 4. #20260485 | C2 | semidirect |
| 5. #20260464 | C2 | semidirect |
| 6. #20260457 | C2 | semidirect |
| 7. D4⋊C8×C97 | C2 | semidirect |
| 25. #13095496 | C8 | semidirect |
| 45. D4×C97 | C2×C8 | semidirect |
| 54. D388 | C2×C8 | semidirect |
| 63. #11715895 | C2×C8 | semidirect |
| 84. C97 | #1580 | semidirect |
| 90. D4⋊C8 | D97 | semidirect |
| 131. D4 | C8×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095496 | 2 |
| D4×#11715895 | 2 |
| #20260800 | 2 |
| #20260485 | 2 |
| #20260464 | 2 |
| #20260457 | 2 |
| D4⋊C8×C97 | 2 |
| #1580 | 97 |