Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
552 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 178 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×Q8×#6923 | C2 | semidirect |
| 3. SD16×#6923 | C2 | direct (N × H) |
| 4. C2×#14519845 | C2 | semidirect |
| 5. C2×#14519840 | C2 | semidirect |
| 7. C2×C8×#6923 | C2 | semidirect |
| 12. Q8×#6923 | C22 | semidirect |
| 21. #14519845 | C22 | semidirect |
| 22. #14519840 | C22 | semidirect |
| 24. C8×#6923 | C22 | semidirect |
| 27. C2×#11758190 | C4 | semidirect |
| 28. C2×#11758200 | C4 | semidirect |
| 29. C2×#11758201 | C4 | semidirect |
| 30. SD16×D61 | C4 | semidirect |
| 33. C2×SD16×C61 | C4 | semidirect |
| 41. C2×Q8×C61 | C2×C4 | semidirect |
| 46. Q8×D61 | C2×C4 | semidirect |
| 56. C2×Dic122 | C2×C4 | semidirect |
| 69. SD16×C61 | C2×C4 | semidirect |
| 70. C2×C8×C61 | C2×C4 | semidirect |
| 71. #11758201 | C2×C4 | semidirect |
| 72. #11758200 | C2×C4 | semidirect |
| 73. C2×#92418 | C2×C4 | semidirect |
| 74. #11758190 | C2×C4 | semidirect |
| 75. C8×D61 | C2×C4 | semidirect |
| 90. C2×#6923 | SD16 | direct (N × H) |
| 94. Q8×C61 | C22×C4 | semidirect |
| 114. Dic122 | C22×C4 | semidirect |
| 116. C8×C61 | C22×C4 | semidirect |
| 117. #92418 | C22×C4 | semidirect |
| 133. #6923 | C2×SD16 | direct (N × H) |
| 142. C2×C61 | C4×SD16 | semidirect |
| 145. D61 | C4×SD16 | semidirect |
| 156. C61 | C2×C4×SD16 | semidirect |
| 165. C2×SD16 | #6923 | direct (N × H) |
| 189. C2×Q8 | C2×#6923 | semidirect |
| 208. SD16 | C2×#6923 | direct (N × H) |
| 215. C2×C8 | C2×#6923 | semidirect |
| 237. Q8 | C22×#6923 | semidirect |
| 265. C8 | C22×#6923 | semidirect |
| 293. C2 | SD16×#6923 | direct (N × H) |