Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
736 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 3. C2×#15690729 | C2 | semidirect |
| 4. C2×#15690728 | C2 | semidirect |
| 5. #101×D97 | C2 | direct (N × H) |
| 6. C2×#101×C97 | C2 | semidirect |
| 21. #15690729 | C22 | semidirect |
| 22. #15690728 | C22 | semidirect |
| 25. #101×C97 | C22 | semidirect |
| 102. C2×D97 | #101 | direct (N × H) |
| 112. C2×C97 | C2×#101 | semidirect |
| 115. D97 | C2×#101 | direct (N × H) |
| 117. C97 | C22×#101 | semidirect |
| 123. C2×#101 | D97 | direct (N × H) |
| 142. #101 | C2×D97 | direct (N × H) |
| 231. C2 | #101×D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D97 | 2 |
| C2×M16×D97 | 2 |
| C2×#15690729 | 2 |
| C2×#15690728 | 2 |
| #101×D97 | 2 |
| C2×#101×C97 | 2 |
| C22×#101 | 97 |