Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
162 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C227 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C227 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C227 ◁ C22×C4×C227 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#41×C227 | C2 | semidirect |
| 2. C2×SD16×C227 | C2 | semidirect |
| 3. C2×D8×C227 | C2 | semidirect |
| 4. #121×C227 | C2 | semidirect |
| 5. #103×C227 | C2 | semidirect |
| 6. #102×C227 | C2 | semidirect |
| 7. C22⋊C8×C227 | C2 | semidirect |
| 27. Q8×C227 | D4 | semidirect |
| 33. D4×C227 | D4 | semidirect |
| 64. C227 | #449 | direct (N × H) |
| 65. #449 | C227 | direct (N × H) |
| 66. C2×#41 | C2×C227 | semidirect |
| 67. C2×SD16 | C2×C227 | semidirect |
| 68. C2×D8 | C2×C227 | semidirect |
| 69. #121 | C2×C227 | semidirect |
| 70. #103 | C2×C227 | semidirect |
| 71. #102 | C2×C227 | semidirect |
| 72. C22⋊C8 | C2×C227 | semidirect |
| 92. Q8 | D4×C227 | semidirect |
| 98. D4 | D4×C227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C227 | 2 |
| C2×SD16×C227 | 2 |
| C2×D8×C227 | 2 |
| #121×C227 | 2 |
| #103×C227 | 2 |
| #102×C227 | 2 |
| C22⋊C8×C227 | 2 |
| #449 | 227 |