Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20261145 | C2 | semidirect |
| 4. #20261144 | C2 | semidirect |
| 5. #20261143 | C2 | semidirect |
| 6. #20261142 | C2 | semidirect |
| 7. #20261141 | C2 | semidirect |
| 11. #501×C97 | C2 | semidirect |
| 53. C8×D97 | Q8 | semidirect |
| 102. C8×C97 | C2×Q8 | semidirect |
| 103. #11715895 | C2×Q8 | semidirect |
| 123. D97 | #501 | direct (N × H) |
| 125. C97 | C2×#501 | semidirect |
| 133. #501 | D97 | direct (N × H) |
| 228. C8 | Q8×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D97 | 2 |
| #125×D97 | 2 |
| #20261145 | 2 |
| #20261144 | 2 |
| #20261143 | 2 |
| #20261142 | 2 |
| #20261141 | 2 |
| #107×D97 | 2 |
| #106×D97 | 2 |
| #97×D97 | 2 |
| #501×C97 | 2 |
| C2×#501 | 97 |