Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×Q16×D17 | C2 | semidirect |
| 3. #11763189 | C2 | semidirect |
| 4. #11763051 | C2 | semidirect |
| 5. #11763019 | C2 | semidirect |
| 6. #11762966 | C2 | semidirect |
| 8. C4×Q16×C17 | C2 | semidirect |
| 37. Q16×C17 | D4 | semidirect |
| 65. D68 | Q16 | direct (N × H) |
| 79. C2×D17 | C2×Q16 | semidirect |
| 83. C4×C17 | C2×Q16 | semidirect |
| 94. C4×Q16 | D17 | semidirect |
| 120. C17 | D4×Q16 | semidirect |
| 132. Q16 | D68 | direct (N × H) |
| 176. C4 | Q16×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D17 | 2 |
| Q8×D68 | 2 |
| #11763189 | 2 |
| #11763051 | 2 |
| #11763019 | 2 |
| #11762966 | 2 |
| C8×D68 | 2 |
| C4×Q16×C17 | 2 |
| D4×Q16 | 17 |