Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#10587605 | C2 | semidirect |
| 2. C2×D8×D17 | C2 | semidirect |
| 3. #11763246 | C2 | direct (N × H) |
| 4. C2×#10587499 | C2 | semidirect |
| 5. C2×D272 | C2 | semidirect |
| 6. C2×#10587497 | C2 | semidirect |
| 7. C2×#10587469 | C2 | semidirect |
| 8. C2×C17×SD32 | C2 | semidirect |
| 11. C2×Q16×C17 | C22 | semidirect |
| 16. #10587605 | C22 | semidirect |
| 18. D8×D17 | C22 | semidirect |
| 20. C2×D136 | C22 | semidirect |
| 22. C17×SD32 | C22 | semidirect |
| 23. C2×C16×C17 | C22 | semidirect |
| 24. #10587499 | C22 | semidirect |
| 25. #10587497 | C22 | semidirect |
| 26. C2×#63214 | C22 | semidirect |
| 27. D272 | C22 | semidirect |
| 28. #10587469 | C22 | semidirect |
| 43. Q16×C17 | C23 | semidirect |
| 53. D136 | C23 | semidirect |
| 56. C16×C17 | C23 | semidirect |
| 57. #63214 | C23 | semidirect |
| 102. C2×SD32 | D17 | semidirect |
| 107. C2×C17 | #509 | semidirect |
| 116. C2×Q16 | C2×D17 | semidirect |
| 126. SD32 | C2×D17 | semidirect |
| 131. C2×C16 | C2×D17 | semidirect |
| 132. C17 | C2×#509 | semidirect |
| 147. Q16 | C22×D17 | semidirect |
| 161. C16 | C22×D17 | semidirect |
| 205. C2 | #11763246 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587605 | 2 |
| C2×D8×D17 | 2 |
| #11763246 | 2 |
| C2×#10587499 | 2 |
| C2×D272 | 2 |
| C2×#10587497 | 2 |
| C2×#10587469 | 2 |
| C2×C17×SD32 | 2 |
| C2×#509 | 17 |