Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #14272243 | C2 | semidirect |
| 2. #14272209 | C2 | semidirect |
| 3. #14272207 | C2 | semidirect |
| 4. D29⋊#108 | C2 | semidirect |
| 5. #14272162 | C2 | semidirect |
| 6. #14272126 | C2 | semidirect |
| 10. #11745348 | C22 | semidirect |
| 15. C2×Q16×C29 | C4 | semidirect |
| 16. C2×#90784 | C4 | semidirect |
| 17. #11745281 | C4 | semidirect |
| 18. #11745281 | C4 | semidirect |
| 21. C2×D232 | C4 | semidirect |
| 23. #11745226 | C22 | semidirect |
| 24. #11745212 | C22 | semidirect |
| 25. #11745211 | C22 | semidirect |
| 26. #11745208 | C22 | semidirect |
| 27. C8×#1181 | C22 | semidirect |
| 114. C2×Q16 | #1181 | semidirect |
| 129. C29 | #2957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272243 | 2 |
| #14272209 | 2 |
| #14272207 | 2 |
| D29⋊#108 | 2 |
| #14272162 | 2 |
| #14272126 | 2 |
| C2×#11745281 | 2 |
| #2957 | 29 |