Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
302 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 2. #14272174 | C2 | semidirect |
| 4. #14272109 | C2 | semidirect |
| 5. #14272042 | C2 | semidirect |
| 6. #14272034 | C2 | semidirect |
| 25. C29×#104 | C4 | semidirect |
| 26. #11745185 | C4 | semidirect |
| 27. #11745173 | C4 | semidirect |
| 28. #11745153 | C4 | semidirect |
| 59. M16×C29 | C2×C4 | semidirect |
| 60. C42×C29 | C2×C4 | semidirect |
| 62. C4×Dic29 | C2×C4 | semidirect |
| 63. #90777 | C2×C4 | semidirect |
| 75. Q8×C29 | C4⋊C4 | semidirect |
| 77. D4×C29 | C4⋊C4 | semidirect |
| 88. D116 | C4⋊C4 | semidirect |
| 99. Dic58 | C4⋊C4 | semidirect |
| 157. #104 | #1181 | semidirect |
| 160. C29 | #1859 | semidirect |
| 180. M16 | C2×#1181 | semidirect |
| 197. C42 | C2×#1181 | semidirect |
| 202. Q8 | C4⋊#1181 | semidirect |
| 209. D4 | C4⋊#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272232 | 2 |
| #14272174 | 2 |
| #14272154 | 2 |
| #14272109 | 2 |
| #14272042 | 2 |
| #14272034 | 2 |
| #104×D29 | 2 |
| #1859 | 29 |