Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
164 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 73 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×#16861148 | C2 | semidirect |
| 3. Dic127⋊C16 | C2 | semidirect |
| 4. C22⋊(C127⋊C16) | C2 | semidirect |
| 5. (C2×D127)⋊C16 | C2 | semidirect |
| 6. #22549651 | C2 | semidirect |
| 7. C22×C16×C127 | C2 | semidirect |
| 39. C16×C127 | D4 | semidirect |
| 59. C22×C127 | M32 | semidirect |
| 76. C127 | #2168 | semidirect |
| 78. C22×C16 | D127 | semidirect |
| 115. C16 | C22⋊D127 | semidirect |
| 138. C22 | #16861148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861148 | 2 |
| C8×C22⋊D127 | 2 |
| Dic127⋊C16 | 2 |
| C22⋊(C127⋊C16) | 2 |
| (C2×D127)⋊C16 | 2 |
| #22549651 | 2 |
| C22×C16×C127 | 2 |
| #2168 | 127 |