Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 161 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. #13093215 | C2 | semidirect |
| 2. #13092984 | C2 | semidirect |
| 3. #13092595 | C2 | semidirect |
| 4. #13092585 | C2 | semidirect |
| 5. #13092434 | C2 | semidirect |
| 6. C2×#10625015 | C2 | semidirect |
| 7. C2×C23×H(5,𝔽2) | C2 | semidirect |
| 16. C2×#67288 | C22 | semidirect |
| 18. #10625122 | C22 | semidirect |
| 20. #10625120 | C22 | semidirect |
| 22. #10625111 | C22 | semidirect |
| 24. #10625107 | C22 | semidirect |
| 26. #10625097 | C22 | semidirect |
| 27. C2×#67267 | C22 | semidirect |
| 28. #10625019 | C22 | semidirect |
| 29. #10625015 | C22 | semidirect |
| 36. #41×C23 | D4 | semidirect |
| 38. C2×Q8×C23 | D4 | semidirect |
| 48. C2×D4×C23 | D4 | semidirect |
| 57. C2×D92 | C23 | semidirect |
| 59. C2×Dic46 | C23 | semidirect |
| 67. C4×Dic23 | C23 | semidirect |
| 69. #67267 | C23 | semidirect |
| 125. C2×H(5,𝔽2) | D23 | semidirect |
| 161. C23 | #3019 | semidirect |
| 170. #41 | C22⋊D23 | semidirect |
| 173. C2×Q8 | C22⋊D23 | semidirect |
| 186. C2×D4 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13093215 | 2 |
| #13092984 | 2 |
| #13092595 | 2 |
| #13092585 | 2 |
| #13092434 | 2 |
| C2×#10625015 | 2 |
| C2×C23×H(5,𝔽2) | 2 |
| #3019 | 23 |