Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
276 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42×C179 | D4 |
| commutator | C4 | C22×C8×C179 |
| Frattini, cosocle | C42 | C23×C179 |
| socle | C22×C179 | C2×C22⋊C4 |
| prime radical | C2×#41×C179 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C179 ◁ C2×C42×C179 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #431×C179 | C2 | semidirect |
| 3. C2×C4×C8×C179 | C2 | semidirect |
| 4. Q8⋊C8×C179 | C2 | semidirect |
| 5. D4⋊C8×C179 | C2 | semidirect |
| 24. #41×C179 | C8 | semidirect |
| 54. Q8×C179 | C2×C8 | semidirect |
| 57. D4×C179 | C2×C8 | semidirect |
| 98. C179 | #1476 | direct (N × H) |
| 99. #1476 | C179 | direct (N × H) |
| 101. #431 | C2×C179 | semidirect |
| 102. C2×C4×C8 | C2×C179 | semidirect |
| 103. Q8⋊C8 | C2×C179 | semidirect |
| 104. D4⋊C8 | C2×C179 | semidirect |
| 123. #41 | C8×C179 | semidirect |
| 153. Q8 | C2×C8×C179 | semidirect |
| 156. D4 | C2×C8×C179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#41×C179 | 2 |
| #431×C179 | 2 |
| C2×C4×C8×C179 | 2 |
| Q8⋊C8×C179 | 2 |
| D4⋊C8×C179 | 2 |
| #1476 | 179 |