Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
952 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C4×C13×C22⋊C4 | C2 |
| hypercenter | C4×C22⋊C4 | D13 |
| hypocenter | C13 | #2431 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6127 | C2 | semidirect |
| 2. C2×#88184 | C2 | semidirect |
| 3. C2×#88129 | C2 | semidirect |
| 4. C2×#88128 | C2 | semidirect |
| 5. C4×C13×C22⋊C4 | C2 | semidirect |
| 6. #11718621 | C2 | semidirect |
| 7. #11718600 | C2 | semidirect |
| 8. #11718590 | C2 | semidirect |
| 9. #11718326 | C2 | semidirect |
| 38. C22×C4×C13 | D4 | semidirect |
| 59. C2×D52 | D4 | semidirect |
| 65. C2×Dic26 | D4 | semidirect |
| 102. C2×C4×C13 | #41 | semidirect |
| 123. C4×C22⋊C4 | D13 | semidirect |
| 209. C22×C4 | D52 | semidirect |
| 221. C13 | #2431 | semidirect |
| 260. C2×C4 | #6127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6127 | 2 |
| C2×#88184 | 2 |
| C2×#88129 | 2 |
| C2×#88128 | 2 |
| C4×C13×C22⋊C4 | 2 |
| #11718621 | 2 |
| #11718600 | 2 |
| #11718590 | 2 |
| #11718326 | 2 |
| #2431 | 13 |