Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
198 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #88192 |
| commutator, cosocle | C42×C13 | C23 |
| Frattini | C42 | C22×D13 |
| Fitting | C13×#493 | C2 |
| socle | C22×C13 | #121 |
| hypercenter | #493 | D13 |
| hypocenter | C13 | #1687 |
| LCS | G ▷ C42×C13 ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#493 | C2 | semidirect |
| 2. #11718733 | C2 | semidirect |
| 3. #11718349 | C2 | semidirect |
| 4. #11718136 | C2 | semidirect |
| 5. #11718049 | C2 | semidirect |
| 49. C8×C13 | D8 | semidirect |
| 52. #493 | D13 | semidirect |
| 101. C13 | #1687 | semidirect |
| 119. C8 | #6104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#493 | 2 |
| #11718733 | 2 |
| #11718349 | 2 |
| #11718136 | 2 |
| #11718049 | 2 |
| #1687 | 13 |