Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
Only the 337 normal subgroups are shown; non-normal subgroups are omitted.
Only the group's 337 normal subgroups are shown; non-normal subgroups are omitted.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72209716 |
| commutator, Frattini, cosocle | C22×Q82 | C24 |
| LCS | G ▷ C22×Q82 ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C22×Q82 ◁ G | |
| LECS | G ▷ C22×Q82 ▷ C24 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72271468 | C2 | semidirect |
| 2. #72271463 | C2 | semidirect |
| 3. #72271461 | C2 | semidirect |
| 4. #72271430 | C2 | semidirect |
| 5. #72271424 | C22 | semidirect |
| 7. #72271377 | C2 | semidirect |
| 8. #72271374 | C22 | semidirect |
| 10. #72268378 | C22 | semidirect |
| 11. #72268193 | C22 | semidirect |
| 12. #72268191 | C22 | semidirect |
| 13. #72268190 | C22 | semidirect |
| 14. 2−1+42 | C22 | semidirect |
| 59. 2−1+4 | #2202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72271468 | 2 |
| #72271463 | 2 |
| #72271461 | 2 |
| #72271430 | 2 |
| #72271377 | 2 |