Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
180 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 71 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. #11763899 | C2 | semidirect |
| 4. #11763898 | C2 | semidirect |
| 32. M16×C17 | C8 | semidirect |
| 33. #63223 | C8 | semidirect |
| 34. #63218 | C8 | semidirect |
| 54. C8×C17 | C2×C8 | semidirect |
| 55. #3622 | C2×C8 | semidirect |
| 93. C17 | #1565 | semidirect |
| 101. M16 | #3633 | semidirect |
| 131. C8 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763922 | 2 |
| C2×C4⋊#3633 | 2 |
| #11763899 | 2 |
| #11763898 | 2 |
| M16×#595 | 2 |
| #1565 | 17 |