Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×Q16×D97 | C2 | semidirect |
| 3. #20261113 | C2 | semidirect |
| 4. #20260976 | C2 | semidirect |
| 5. #20260973 | C2 | semidirect |
| 6. #20260943 | C2 | semidirect |
| 7. #20260891 | C2 | semidirect |
| 8. #20260889 | C2 | semidirect |
| 9. Q16×Dic97 | C2 | semidirect |
| 11. C22×Q16×C97 | C2 | semidirect |
| 76. Q16×C97 | D4 | semidirect |
| 94. C22⋊D97 | Q16 | direct (N × H) |
| 112. C22×C97 | C2×Q16 | semidirect |
| 116. C2×D97 | C2×Q16 | semidirect |
| 126. Dic97 | C2×Q16 | semidirect |
| 133. C97 | D4×Q16 | semidirect |
| 135. C22×Q16 | D97 | semidirect |
| 193. Q16 | C22⋊D97 | direct (N × H) |
| 248. C22 | Q16×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D97 | 2 |
| Q8×C22⋊D97 | 2 |
| #20261113 | 2 |
| #20260976 | 2 |
| #20260973 | 2 |
| #20260943 | 2 |
| #20260891 | 2 |
| #20260889 | 2 |
| Q16×Dic97 | 2 |
| C8×C22⋊D97 | 2 |
| C22×Q16×C97 | 2 |
| D4×Q16 | 97 |