Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
948 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 205 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×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C4×C11×C4⋊C4 | C2 |
| hypercenter | C4×C4⋊C4 | D11 |
| hypocenter | C11 | #2541 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#66948 | C2 | semidirect |
| 2. C2×#66927 | C2 | semidirect |
| 3. C2×#66927 | C2 | semidirect |
| 4. C2×C4×D44 | C2 | semidirect |
| 5. C4×C11×C4⋊C4 | C2 | semidirect |
| 6. #10622552 | C2 | semidirect |
| 7. #10622284 | C2 | semidirect |
| 44. C2×D44 | D4 | semidirect |
| 47. C11×C4⋊C4 | D4 | semidirect |
| 49. C42×C11 | D4 | semidirect |
| 89. C4×C4⋊C4 | D11 | semidirect |
| 107. C4×C11 | #121 | semidirect |
| 108. C4×C11 | #127 | semidirect |
| 157. C4⋊C4 | D44 | semidirect |
| 161. C42 | D44 | semidirect |
| 162. C11 | #2541 | semidirect |
| 210. C4 | #66927 | semidirect |
| 211. C4 | #66948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66948 | 2 |
| C2×#66927 | 2 |
| C2×C4×D44 | 2 |
| C4×C11×C4⋊C4 | 2 |
| #10622552 | 2 |
| #10622284 | 2 |
| #2541 | 11 |