Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
224 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×C16×D97 | C2 | semidirect |
| 3. #108×D97 | C2 | semidirect |
| 4. #20260543 | C2 | semidirect |
| 5. #20260542 | C2 | semidirect |
| 6. #20260541 | C2 | semidirect |
| 7. #359×C97 | C2 | semidirect |
| 19. C2×#13095486 | C22 | semidirect |
| 22. #15690746 | C22 | semidirect |
| 25. C2×C16×C97 | C22 | semidirect |
| 26. #108×C97 | C22 | semidirect |
| 107. D97 | #359 | direct (N × H) |
| 109. C97 | C2×#359 | semidirect |
| 116. #359 | D97 | direct (N × H) |
| 132. C2×C16 | C2×D97 | semidirect |
| 135. #108 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D97 | 2 |
| C2×C16×D97 | 2 |
| #108×D97 | 2 |
| #20260543 | 2 |
| #20260542 | 2 |
| #20260541 | 2 |
| #359×C97 | 2 |
| C2×#359 | 97 |