Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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×#15690755 | C2 | semidirect |
| 2. #20260976 | C2 | semidirect |
| 4. #20260563 | C2 | semidirect |
| 5. #20260540 | C2 | semidirect |
| 6. #20260537 | C2 | semidirect |
| 7. C22×C16×C97 | C2 | semidirect |
| 39. C16×C97 | D4 | semidirect |
| 59. C22×C97 | SD32 | semidirect |
| 76. C97 | #2217 | semidirect |
| 78. C22×C16 | D97 | semidirect |
| 115. C16 | C22⋊D97 | semidirect |
| 138. C22 | #15690755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690755 | 2 |
| #20260976 | 2 |
| #20260971 | 2 |
| #20260563 | 2 |
| #20260540 | 2 |
| #20260537 | 2 |
| C22×C16×C97 | 2 |
| #2217 | 97 |